Cracking The Ap Calculus ab Exam 2018

Here we will use the Power Rule, which says that ∫ xn dx = + C. First, let’s simplify the

integrand: ∫ dx = ∫ dx = ∫ (x^3 + 7 x−2) dx. Now, we can evaluate the

integral: ∫(x^3 + 7x−2) dx = + C.

2. − 2x + C

Here we will use the Power Rule, which says that ∫ xn dx = + C. First, let’s simplify the

integrand: ∫(1 + x^2 )(x − 2) dx = ∫(x^3 − 2x^2 + x − 2) dx. Now, we can evaluate the integral: ∫(x^3

−   2x^2    +   x   −   2)  dx  =       −   2x  +   C.

3. sin x + 5 cos x + C

Here    we  will    use the Rules   for the Integrals   of  Trig    Functions,  namely:

(^) ∫sin x dx = − cos x + C and ∫cos x dx = sin x + C. We get ∫(cos x − 5 sin x) dx = sin x + 5 cos
x + C.

4. sec x + C

Here we will use the Rules for the Integrals of Trig Functions, namely, ∫(sec x tan x) dx = sec x

+ C. First, we need to rewrite the integrand, using trig identities: ∫ dx = ∫

dx = ∫(sec x tan x) dx. Now, we can evaluate the integral: ∫(sec x tan x) dx =

sec x   +   C.

5. tan x − x + C

Here we will use the Rules for the Integrals of Trig Functions, namely, ∫sec^2 x dx = tan x + C.

First, we need to rewrite the integrand, using trig identities: ∫(tan^2 x) dx = ∫(sec^2 x − 1) dx.

Now, we can evaluate the integral: ∫(sec^2 x − 1) dx = tan x − x + C.