Question

Suppose G(x) is an antiderivative of (cosx/e^x) and G(-2) = -1. Then, G(5) =?

(A)-3.485
(B) -1.002
(C) 0.371
(D) 1.847
(E) 0.818

apparently the answer is E but i dont know why. I have trouble with integrals pls help

 

Answer 1

Step 1:

The function is and .

Consider.

Rewrite the above integral.

Use integration by parts :.

Assume and .

and .

Substitute , , and in .

               equation (1)

Now consider.

Use integration by parts :.

Assume and .

and .

Substitute , , and in .

Substitute in equation (1).

.

Solution :

.

Answer 2

Contd....

Step 2:

Therefore .

Condition is .

Substitute in .

Convert radians into degrees.

Step 3:

Find .

Substitute and in .

Solution :

.