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I’m working on a test where is about 10 questions long, I need all the work to be shown so I can learn from it. and where it can help me better understand.

(1) Perform the following integrals. Show your work to get full credit. You can

use the

R formulas on the reference sheet in solving these problems.

(a) R x cos(x2 )dx

(b) R x2 cos x dx

(c) e2x cos xdx

R x2

(d) √1+x

dx

2

R π/4

(e) 0

sin2 x cos3 x dx

R 3

2

+3x+36

dx

(f) x +6x

R ln x x3 +9x

√ dx

(g)

R x 1

(h) (x2 +6x+25)

3/2 dx

(2) Use the first form of the fundamental theorem of calculus to write a formula

for a function f (x) satisfying

f 0 (x) = arctan cos x2

f (5) = 0

Your formula should include an integral. Do not attempt to evaluate or

simplify the integral.

R x2 1

0

(3) Let f (x) = 2 1+cos

t dt. Find f (x).

1

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