Question
If f : R →R; f(x) = sin x + x, then the value of 
(f-1 (x)) dx, is equal to
- p2
- None of these
Hint:
The calculation of an integral is known as integration. Numerous important quantities in mathematics, such as areas, volumes, displacement, etc., can be found using integrals. Apart from differentiation, one of the two main calculus topics in mathematics is integration (which measure the rate of change of any function with respect to its variables). Here we have to find (f-1 (x)) dx.
The correct answer is:
The summing of discrete data is indicated by the integration. To determine the functions that will characterise the area, displacement, and volume that result from a combination of small data that cannot be measured separately, integrals are calculated.
We are aware that differentiation is the process of discovering a function's derivative and integration is the process of discovering a function's antiderivative. Thus, both processes are the antithesis of one another. Therefore, we can say that differentiation is the process of differentiation and integration is the reverse.
Here we have given the function f : R →R; f(x) = sin x + x
Here we used the concept of integration and the inverse functions to solve the question. Finding an antiderivative of a function is the procedure known as integration. The process of adding the slices to complete it is comparable. The process of integration is the opposite of that of differentiation. So the final answer is 
.
Related Questions to study
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and 
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The polar equation of the straight line with intercepts 'a' and 'b' on the rays and respectively is
The polar equation of the straight line parallel to the initial line and at a distance of 4 units above the initial line is
The polar equation of the straight line parallel to the initial line and at a distance of 4 units above the initial line is
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The polar equation of axy is
If x, y, z are integers and x 
0, y 1, z 2, x + y + z = 15, then the number of values of the ordered triplet (x, y, z) is -
If x, y, z are integers and x 0, y 1, z 2, x + y + z = 15, then the number of values of the ordered triplet (x, y, z) is -
If 
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Here we used the concept of quadratic equations and solved the problem. We also understood the concept of discriminant and used it in the solution to find the intervals. Therefore, total 7 seven solutions are possible so 7 equations can be formed.
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ax2 + bx + c = 0 has real and distinct roots null. Further a > 0, b < 0 and c < 0, then –
Here we used the concept of quadratic equations and solved the problem. The concept of sum of roots and product of roots was also used here. Therefore, 0 < ∣α∣ < β.
ax2 + bx + c = 0 has real and distinct roots null. Further a > 0, b < 0 and c < 0, then –
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is
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The cartesian equation of is
Here we used the concept of quadratic equations and solved the problem. We also understood the concept of trigonometric ratios and used the formula to find the equation. So the equation is .
The castesian equation of 
is
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The castesian equation of is
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is
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