Compute the integral (a) int sin (pi x) dx by letting u = pi x. (b) int e^(x/2) dx by letting u = x/2. Show that you got the correct answer by differentiating the computed function.

(a)

(b)

Step-by-step explanation:

(a)

Let u = π x

differentiating with respect to x

du = π dx

Putting the value of x and dx

   [ c is an arbitrary constant]

Now putting the value of u

(b)

Let

differentiating with respect to x

2du = dx

Putting the value of x and dx

=

=

Now putting the value of u

      [ c is an arbitrary constant]