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]

if farmer matt works for 8 hours a day, how many days will it take him to completely plant 12 rows of crops? each batch of cookies needs 3/4 cups of sugar.

step-by-step explanation:

no oblique asymptote

step-by-step explanation:

to find the oblique asymptote of f(x)

here numerator has degree 1 and denomintor degree 2

degree of numerator < degree of denominator

hence there is no oblique asymptote

when the degree of the denominator > that of the numerator, we saw that the value in the denominator got so much bigger, so quickly,   giving us a horizontal asymptote of the x-axis. or we can write

f(x) = a polynomial of x + a proper fraction.

in this case only we have oblique asymptotes but not when numerator has less degree.