Maths-
General
Easy
Question
The indefinite integral of
is, for any arbitrary constant -
The correct answer is: ![1 divided by 13 l o g invisible function application open vertical bar t a n invisible function application open parentheses fraction numerator x over denominator 2 end fraction plus fraction numerator 1 over denominator 2 end fraction t a n to the power of negative 1 end exponent invisible function application fraction numerator 12 over denominator 5 end fraction close parentheses close vertical bar plus c](data:image/png;base64,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)
Related Questions to study
maths-
If f
= x + 2 then
is equal to
If f
= x + 2 then
is equal to
maths-General
maths-
Let
, then
is equal to:
Let
, then
is equal to:
maths-General
maths-
Statement I : y = f(x) =
, x
R Range of f(x) is [3/4, 1)
Statement II :
.
Statement I : y = f(x) =
, x
R Range of f(x) is [3/4, 1)
Statement II :
.
maths-General
maths-
Statement I : Function f(x) = sinx + {x} is periodic with period ![2 pi](data:image/png;base64,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)
Statement II : sin x and {x} are both periodic with period
and 1 respectively.
Statement I : Function f(x) = sinx + {x} is periodic with period ![2 pi](data:image/png;base64,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)
Statement II : sin x and {x} are both periodic with period
and 1 respectively.
maths-General
maths-
Statement 1 : f : R
R and
is bijective.
Statement 2 :
is bijective.
Statement 1 : f : R
R and
is bijective.
Statement 2 :
is bijective.
maths-General
maths-
Statement I : Graph of y = tan x is symmetrical about origin
Statement II : Graph of
is symmetrical about y-axis
Statement I : Graph of y = tan x is symmetrical about origin
Statement II : Graph of
is symmetrical about y-axis
maths-General
maths-
Statement-
If
Where
is an identity function.
Statement-
R defined by
is an identity function.
Statement-
If
Where
is an identity function.
Statement-
R defined by
is an identity function.
maths-General
Maths-
Assertion (A) :
Graph of ![open curly brackets left parenthesis x comma y right parenthesis divided by y equals 2 to the power of negative x end exponent text and end text x comma y element of R close curly brackets](data:image/png;base64,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)
Reason (R) : In the expression am/n, where a, m, n × J+, m represents the power to which a is be raised, whereas n determines the root to be taken; these two processes may be administered in either order with the same result.
Assertion (A) :
Graph of ![open curly brackets left parenthesis x comma y right parenthesis divided by y equals 2 to the power of negative x end exponent text and end text x comma y element of R close curly brackets](data:image/png;base64,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)
Reason (R) : In the expression am/n, where a, m, n × J+, m represents the power to which a is be raised, whereas n determines the root to be taken; these two processes may be administered in either order with the same result.
Maths-General
maths-
Assertion: The period of
is 1/2.
Reason: The period of x – [x] is 1.
Assertion: The period of
is 1/2.
Reason: The period of x – [x] is 1.
maths-General
Maths-
Assertion : Fundamental period of
.
Reason : If the period of f(x) is
and the period of g(x) is
, then the fundamental period of f(x) + g(x) is the L.C.M. of
and T
Assertion : Fundamental period of
.
Reason : If the period of f(x) is
and the period of g(x) is
, then the fundamental period of f(x) + g(x) is the L.C.M. of
and T
Maths-General
Maths-
Assertion: The function defined by
is invertible if and only if
.
Reason: A function is invertible if and only if it is one-to-one and onto function.
Assertion: The function defined by
is invertible if and only if
.
Reason: A function is invertible if and only if it is one-to-one and onto function.
Maths-General
Maths-
Assertion :
can never become positive.
Reason : f(x) = sgn x is always a positive function.
Assertion :
can never become positive.
Reason : f(x) = sgn x is always a positive function.
Maths-General
Maths-
If f (x) = ![open curly brackets table row cell e to the power of cos invisible function application x end exponent end cell cell sin invisible function application x text for end text vertical line x vertical line less or equal than 2 end cell row cell text 2, end text end cell cell text otherwise end text end cell end table comma text then end text not stretchy integral subscript text -2 end text end subscript superscript 3 end superscript f left parenthesis x right parenthesis d x equals close](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAATwAAAAtCAYAAAAz+NeMAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAc1CXO0QAACZBJREFUeNrtXX9kHUkcH09URYSIqKg4oqqiKpyKc6pKVVVElTp14lSoOFF1Sp1Tp+qoOnGqStWpqhNOVFVFqYhTUaUqqqqOOFVV/ScqqiLCu/nKZ73NvJndmd3Z9/bH98PIy77d2Xnfnf3M9/ud+c5XCD2mZHklGAxG3lBHWZdlSZYjLJJ0mJPlkSxDLAoGI9fYI8tbFkNyTMrylMXAYBQCNVlWWAzJ8USWURYDg5F79MpyXZbTLIrkWJOlw2N9PTCRyd9QDx3vk2Velk/42xf67oQs72TZUK4JCHlfaHQj0/srfmyxqOesHkb650BlnEWRrw59Q2xOgNSU4zdluYDPF3BegNUIEiPtcwafp0GODCa8KqJblt9kOcOiyE+HXtGQXXC8C587oekFeAMS3G6ok2amzslyqwC/34SjsiwbtNiqEd63ssxioAtmHr+v8DtIVtGfsnyEPGYN71DYKmPkpENvWN5nPfSZZp4WZfkAYlBxDaS4rcCERzNrQwV8rlnI5x9ZToUGwCE8/1MVfQfJTUMunUFZzsryXpj96gdkec60lZ8OTaTVEaPhdSkaXoBjuD6MwzBpX4utfr+qyznvhPeNLAsO55NL42UF379RyPgHWQbwmci/V3kGdWh27MNucYfeAZV7DVrLQeX732X5WXPdDdHw4f0iNn16KvYqhDcAbYAI8kdZLju2dRAv3ZdQp4n7/cH/J2GCrqENA5prJ2S5ojl+Gd+pHVbXhlGQ+Tr+jhnaSPe/DTNwI8VztW1z0v4REN08PrugiqbaIp59oCTUmJLyQ3jdGIXHQqaIGp1B5DQnmn1VvaIxS/vYMIK9DZm0ZL7SDO3u0P/LIS3RBs8NBBJHeER2V0Mj6WmQng4vMAiI0LnXLeU8gt+0N0T4yxqiqIMMJxzM+qjnattml/6RhuiC6xcr9u51Q74LTEP5JLyrGu3tocjGt+YDpNn1JCC8Q8qxmtjqcwyDCHo6ZH7PO8h5VuOrof/va6792uNztW2zTf8IiG4hIdERaLLqmdiczKgSjkO+twQjd4RXg3bWpxxbzbEaflzEO8PrlvKIktNjmPZLiuYad/2qZrDYhuNpzEqba2zabFMPff9TimfUA4KvYnzoJciPFxLnkPBGRLMvql4AM6QLI+jrkHnsm/DOQQPc5yhnU53rLSA8mzZnreENgux2VfTd+xvy5UinHBLeGB5QUUGm+IsMCC9YUzbtqEm2U8OzbbPLvV2Jbw8Gos4Kv3tLkO+eFt+XJgCvOF5zBddVhvCoEz8r8O80+eHSEB5pKA/w0pIm+dzRpJ0VzZMqZIbfy5DwXNqc5N7hyYsRwzk7MHh2iGqDZqU3RHYuoZrYOjkloNEn3Sxk0cIiKA3hCZiF5yDIHmhNBwryOyeEfjYsKeGRL3NOIQsyTe46yHm/2JyVHQp1xmXR7Lz3RXiubU5674D4Hhu+e9gCrSbvIXFdaOOnjOqniakVlFehwYVIazhhnTRx9sTxmi8iZz5+l44xiB+8IRrLJPJO5nW0l170fk+Etw1a2E7NeTNCHy1iqpcI5w20z1fQ8Hy8vHWNqeza5qyIox5RXLFSUMI7gjY+yqBuIrf3IWILBtRhkd7n/kTYrxgg3+zLPJICo3xoVaTFWkxp1+/Me78+iTbOZFD3CUO9tKxsKmXdFPpm6/87ntHvY8JjtI3w8qDB1yM0dQpXfCqiI2Zo4uYdzqFolu2Gumyib2wxiXpvZCCXX0UjqikM0iZ1LiiX6BtyVcwbTPRrMNFJPuSfvq60wzXKxzvIp8PbRTPhFXlAjNLwJuDKCPyFuoiZEbgUiLzI10RbL01r6nKJvrHBLdGIofWJe8ogEJ6F160KCGAbfaNbRUByW8A19LkbpFvXuGhconzi3B9ObpAOqJuHmRtKibWc1dMOwvtL82KuawhCXZrzQVOXS/SNDWYMhOADbwzaZ1QMtkv0jfq7Lxo0yn9Fs8/Y5T5ecRujFoNRRk22LvT7K6rnfxbNSzdWHe6RFHO43rfCQUT8xfBd3KYTttE3KuG9E80x7lHtsL2Pd8GQnc0p3xhlJTyb4zZmUhaE9wnXd3uWx4gwb0YQZdISbKJvVJN22GDaR7XDNsrHq0lLYB8eo+qER8taOj3fw0bZ2BB223y54hSsN5NmZdqgwTb6Rp20oBnhuw7tcInyaWmHYTCKgHWhX9hqS1L0Uk4kfEeSvju9uPZjBvKgmVJTzgvTshSX6Jsp1BOAfJC6kNO7mna4Rvkw4TEqDZ2jf8mgKdiSFC2OpaUmgWuHZmHvZEx4R3HtgwxkRJMwxwzf6RYeu0bfqAuPibxei8YiZ/qOImneK+1IEuXDhMdgwlMI7xA0pTR+t/0gAjIxKdplLGPC+w7X3slARmSib4/4ntYkBr4z1+gbU2jZDtSzhvoPKe1IGuXDhMdg0ovQYIqCYB+8857rJS3qQ8w5vHkAv0OMgmBYbA2EL5OmmhZ/iM31dzZhX5PCfXso8tuVIh8u5x2t9qBSpAFvp2heM1dELEDuPrOPkbnJSerb1OGrmne0iDt3sIbfepCv6zOLodwdvgp5R4u6cwejddgtstslhZGzEb7IeUfj8se2cucONUctrWdSN9TshMap+rtoBfz9iOdvk8s3ro2MraBZyyB/8xRkOsZiKTfhFTnvqEv+WJOMfe7coeaopaxhl5TzJtBG1XdKzu3xiDbH5fK1aSOjgYuQ8UPIiyZdllK+r3UMvPQ+7WIR54/wip531CV/rEnGPnfuUHecJWf+f8oxWi9F65vU3SjUQG+1zXG5fG3ayGjgMvr+OPoLaeU+lnZQ/6GkOi9YxPkivDLkHU2bXawVO3eEs4XtEo21VvRCBLOBB6FpRNUXl8vXpo2MBjpAemT6X4DLwCfWWMT5Ibyy5B1Nmz+2FTt3kGl5LaRVnMXn8zCrCDdF84aTuvqicvn6ykXBSI+DIt0mpEx4HlGmvKM+NDyb42l27uiBaVmDeduH4wP4n45/1JirUc9fl8t3RVQ7l2yW76HLYNIPTXyQRdd+witb3lHb/LHt3LlDQJumFfRzyvFFw/G4+nR+Rps2MrLFbrgm+lkUyXwAvonJNu9olttc+4Rt/th27twhcG8iqHHl+BSOn3YkPF0uX5s2MrJDPwaubhZFMtBs3mib1POiEJ4Qdvlj27lzh8DARWa2OkHSh3b3WLTBJpdvXBsZ2WFOZJ/EvNQ4I9q7Pq4Mu18wGK0CTxh5GjUetGHkKMvuFwwGo2CYBPm0EmXZ/YLBYOQU/wMNcV0xCW5b4QAAAoV0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWZlbmNlZCBjbG9zZT0iIiBvcGVuPSJ7IiBzZXBhcmF0b3JzPSJ8Ij48bXJvdz48bXRhYmxlPjxtdHI+PG10ZD48bXN1cD48bWk+ZTwvbWk+PG1yb3c+PG1pPmNvczwvbWk+PG1vPiYjeDIwNjE7PC9tbz48bWk+eDwvbWk+PC9tcm93PjwvbXN1cD48L210ZD48bXRkPjxtaT5zaW48L21pPjxtbz4mI3gyMDYxOzwvbW8+PG1pPng8L21pPjxtdGV4dD5mb3ImI3hBMDs8L210ZXh0Pjxtbz58PC9tbz48bWk+eDwvbWk+PG1vPnw8L21vPjxtbz4mI3gyMjY0OzwvbW8+PG1uPjI8L21uPjwvbXRkPjwvbXRyPjxtdHI+PG10ZD48bXRleHQ+Miw8L210ZXh0PjwvbXRkPjxtdGQ+PG10ZXh0Pm90aGVyd2lzZTwvbXRleHQ+PC9tdGQ+PC9tdHI+PC9tdGFibGU+PG1vPiw8L21vPjxtdGV4dD50aGVuJiN4QTA7PC9tdGV4dD48bXN1YnN1cD48bW8+JiN4MjIyQjs8L21vPjxtdGV4dD4tMjwvbXRleHQ+PG1uPjM8L21uPjwvbXN1YnN1cD48bXJvdz48bWk+ZjwvbWk+PG1pPiYjeDIwMEI7PC9taT48bW8+KDwvbW8+PG1pPng8L21pPjxtbz4pPC9tbz48bWk+ZDwvbWk+PG1pPng8L21pPjxtbz49PC9tbz48L21yb3c+PC9tcm93PjwvbWZlbmNlZD48L21hdGg+hO9ZVAAAAABJRU5ErkJggg==)
If f (x) = ![open curly brackets table row cell e to the power of cos invisible function application x end exponent end cell cell sin invisible function application x text for end text vertical line x vertical line less or equal than 2 end cell row cell text 2, end text end cell cell text otherwise end text end cell end table comma text then end text not stretchy integral subscript text -2 end text end subscript superscript 3 end superscript f left parenthesis x right parenthesis d x equals close](data:image/png;base64,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)
Maths-General
Maths-
The value of the integral
dx is :
The value of the integral
dx is :
Maths-General
Maths-
Assertion : Let
be a function defined by f(x) =
. Then f is many-one function.
Reason : If either
or
domain of f, then y = f(x) is one-one function.</span
Assertion : Let
be a function defined by f(x) =
. Then f is many-one function.
Reason : If either
or
domain of f, then y = f(x) is one-one function.</span
Maths-General