Question

Hint:

### 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. The anti-differentiation is another name for the integration.

Here we have given: and we have to integrate it. We will use the formula to find the answer.

## The correct answer is:

### Now we have given the function as . Here the lower limit is and upper limit is . We know that there are some integrals of special functions which makes problem to solve easily. We will use one of them.

We will use substitution method.

So as per the question, we have:

.

So here we used the concept of integrals of special functions and simplified it. We can also solve it manually but it will take lot of time to come to final answer hence we used the special case and the formula of that. The integral of the given function is .

### Related Questions to study

=

>>>Integration of 1 becomes x and integration of e-x becomes -e-x.

>>> =

= (2-)

=

>>>Integration of 1 becomes x and integration of e-x becomes -e-x.

>>> =

= (2-)

So here we used the concept of integrals of special functions and simplified it. We can also solve it manually but it will take lot of time to come to the final answer hence we will use trigonometric formulas. The integral of the given function is

So here we used the concept of integrals of special functions and simplified it. We can also solve it manually but it will take lot of time to come to the final answer hence we will use trigonometric formulas. The integral of the given function is