De Anza College Integral Calculus Math Solved Practice


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

R π/4
(e) 0
sin2 x cos3 x dx
R 3
(f) x +6x
R ln x x3 +9x
√ dx
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
(3) Let f (x) = 2 1+cos
t dt. Find f (x).

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