Maths-
General
Easy

Question

If not stretchy integral subscript blank superscript blank fraction numerator 2 s i n x plus 3 c o s x over denominator blank c o s blank x left parenthesis s i n to the power of 2 end exponent x plus 2 c o s to the power of 2 end exponent x right parenthesis end fraction d x equals logvertical linef(x)vertical line plus lambda t a n to the power of negative 1 end exponent left parenthesis fraction numerator blank t a n blank x over denominator square root of 2 end fraction right parenthesis plus c comma then left parenthesis lambda f right parenthesis equals

  1. left parenthesis fraction numerator 3 over denominator square root of 2 end fraction comma blank t a n to the power of 2 end exponent x plus 2 right parenthesis    
  2. left parenthesis fraction numerator 3 over denominator 2 end fraction comma blank t a n to the power of 2 end exponent x plus 3 right parenthesis    
  3. left parenthesis fraction numerator square root of 3 over denominator 2 end fraction comma blank t a n to the power of 2 end exponent x plus 2 right parenthesis    
  4. left parenthesis fraction numerator 3 over denominator 2 end fraction comma blank t a n to the power of 2 end exponent x plus 2 right parenthesis    

The correct answer is: left parenthesis fraction numerator 3 over denominator square root of 2 end fraction comma blank t a n to the power of 2 end exponent x plus 2 right parenthesis


    not stretchy integral subscript blank superscript blank fraction numerator 2 s i n x plus 3 c o s x over denominator c o s x left parenthesis s i n to the power of 2 end exponent x plus 2 c o s to the power of 2 end exponent x right parenthesis end fraction d x
    equals not stretchy integral subscript blank superscript blank fraction numerator c o s x left parenthesis 2 blank t a n blank x plus 3 right parenthesis over denominator c o s to the power of 3 end exponent x left parenthesis t a n to the power of 2 end exponent x plus 2 right parenthesis end fraction d x
    equals not stretchy integral subscript blank superscript blank fraction numerator left parenthesis 2 blank t a n blank x plus 3 right parenthesis over denominator left parenthesis t a n to the power of 2 end exponent x plus 2 right parenthesis end fraction. s e c to the power of z subscript X end subscript end exponent d x
    t a n blank x equals t rightwards double arrow s e c to the power of 2 end exponent x d x equals d t
    equals not stretchy integral subscript blank superscript blank fraction numerator 2 t plus 3 over denominator t to the power of 2 end exponent plus 2 end fraction. d t
    equals not stretchy integral subscript blank superscript blank fraction numerator 2 t over denominator t to the power of 2 end exponent plus 2 end fraction. d t plus 3 not stretchy integral subscript blank superscript blank fraction numerator 1 over denominator t to the power of 2 end exponent plus left parenthesis square root of 2 right parenthesis to the power of 2 end exponent end fraction. d t
    equals blank l o g blank vertical line t to the power of 2 end exponent plus 2 vertical line plus 3 fraction numerator 1 over denominator square root of 2 end fraction t a n to the power of negative 1 end exponent left parenthesis fraction numerator t over denominator square root of 2 end fraction right parenthesis plus c
    equals blank l o g blank vertical line t a n to the power of 2 end exponent x plus 2 vertical line plus fraction numerator 3 over denominator square root of 2 end fraction t a n to the power of negative 1 end exponent left parenthesis fraction numerator blank t a n blank x over denominator square root of 2 end fraction right parenthesis plus c left parenthesis lambda f blank equals left parenthesis fraction numerator 3 over denominator square root of 2 end fraction comma blank t a n to the power of 2 end exponent x plus 2 right parenthesis

    Related Questions to study

    General
    Maths-

    An incomplete frequency distribution is given below Median value is 46, the missing frequency is

    An incomplete frequency distribution is given below Median value is 46, the missing frequency is

    Maths-General
    General
    Physics-

    In the adjacent diagram, CP represents a wave front and AO & BP, the corresponding two rays. Find the condition on q for constructive interference at P between the ray BP and reflected ray OP

    In the adjacent diagram, CP represents a wave front and AO & BP, the corresponding two rays. Find the condition on q for constructive interference at P between the ray BP and reflected ray OP

    Physics-General
    General
    Physics-

    A thin slice is cut out of a glass cylinder along a plane parallel to its axis. The slice is placed on a flat glass plate as shown. The observed interference fringes from this combination shall be

    A thin slice is cut out of a glass cylinder along a plane parallel to its axis. The slice is placed on a flat glass plate as shown. The observed interference fringes from this combination shall be

    Physics-General
    parallel
    General
    Physics-

    A ray of light of intensity I is incident on a parallel glass-slab at a point A as shown in fig. It undergoes partial reflection and refraction. At each reflection 25% of incident energy is reflected. The rays AB and A'B' undergo interference. The ratio I m i n subscript m a x end subscript is

    A ray of light of intensity I is incident on a parallel glass-slab at a point A as shown in fig. It undergoes partial reflection and refraction. At each reflection 25% of incident energy is reflected. The rays AB and A'B' undergo interference. The ratio I m i n subscript m a x end subscript is

    Physics-General
    General
    Physics-

    AB is incident wave front on mirror R and mirror S whereas PQ and P ´ Q ´ is reflected wave front from mirror R and mirror S respectively. Choose the correct statement

    AB is incident wave front on mirror R and mirror S whereas PQ and P ´ Q ´ is reflected wave front from mirror R and mirror S respectively. Choose the correct statement

    Physics-General
    General
    Physics-

    In the diagram shown, the separation between the slit is equal to 3 lambda comma where lambda is the wavelength of the light incident on the plane of the slits A thin film of thickness 3 lambda and refractive index 2 has been placed in the front of the upper slit. Assuming D greater than greater than lambda the distance of the central maxima on the screen from O is:

    In the diagram shown, the separation between the slit is equal to 3 lambda comma where lambda is the wavelength of the light incident on the plane of the slits A thin film of thickness 3 lambda and refractive index 2 has been placed in the front of the upper slit. Assuming D greater than greater than lambda the distance of the central maxima on the screen from O is:

    Physics-General
    parallel
    General
    Physics-

    Three weight A, B and C are connected by string as shown in the figure. The system moves over a frictionless pulley. The tension in the string connecting A and B is (where g is acceleration due to gravity)

    Three weight A, B and C are connected by string as shown in the figure. The system moves over a frictionless pulley. The tension in the string connecting A and B is (where g is acceleration due to gravity)

    Physics-General
    General
    Physics-

    As shown in the figure, two equal masses each of 2 kg are suspended from a spring balance. The reading of the spring balance will be

    As shown in the figure, two equal masses each of 2 kg are suspended from a spring balance. The reading of the spring balance will be

    Physics-General
    General
    Physics-

    Figures I, II, III and IV depict variation of force with time
    I) 
    II) 
    III) 
    IV) 
    The impulse is highest in the case of situations depicted. Figure

    Figures I, II, III and IV depict variation of force with time
    I) 
    II) 
    III) 
    IV) 
    The impulse is highest in the case of situations depicted. Figure

    Physics-General
    parallel
    General
    Physics-

    The variation of momentum with time of one of the body in a two body collision is shown in fig. The instantaneous force is maximum corresponding to point

    The variation of momentum with time of one of the body in a two body collision is shown in fig. The instantaneous force is maximum corresponding to point

    Physics-General
    General
    Physics-

    A body of mass 3kg is acted on by a force which varies as shown in the graph below. The momentum acquired is given by

    A body of mass 3kg is acted on by a force which varies as shown in the graph below. The momentum acquired is given by

    Physics-General
    General
    Physics-

    A particle of mass m, initially at rest, is acted upon by a variable force F for a brief interval of time T. It begins to move with a velocity u after the force stops acting. F is shown in the graph as a function of time. The curve is a semicircle.

    A particle of mass m, initially at rest, is acted upon by a variable force F for a brief interval of time T. It begins to move with a velocity u after the force stops acting. F is shown in the graph as a function of time. The curve is a semicircle.

    Physics-General
    parallel
    General
    Physics-

    A particle of mass m moving with velocity u makes an elastic one dimensional collision with a stationary particle of mass m. They are in contact for a very short time T. Their force of interaction increases from zero to F0 linearly in time T/2, and decreases linearly to zero in further time T/2. The magnitude of F0 is

    A particle of mass m moving with velocity u makes an elastic one dimensional collision with a stationary particle of mass m. They are in contact for a very short time T. Their force of interaction increases from zero to F0 linearly in time T/2, and decreases linearly to zero in further time T/2. The magnitude of F0 is

    Physics-General
    General
    Physics-

    A body of 2 kg has an initial speed 5ms–1. A force acts on it for some time in the direction of motion. The force time graph is shown in figure. The final speed of the body.

    A body of 2 kg has an initial speed 5ms–1. A force acts on it for some time in the direction of motion. The force time graph is shown in figure. The final speed of the body.

    Physics-General
    General
    Physics-

    In the figure given below, the position-time graph of a particle of mass 0.1 Kg is shown. The impulse at t equals 2 s e c is

    In the figure given below, the position-time graph of a particle of mass 0.1 Kg is shown. The impulse at t equals 2 s e c is

    Physics-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.