Randolph College
Department of Mathematics and Computer Science

 

Homework # 6 - Math 1150


The problems on this homework must be done alone.  The honor code is in effect.

You may submit the solutions twice, if you wish.

 First Name:  Last Name:

 

1. \(\int \cos^3 x dx \)

a.  \(\frac{1}{4}\cos^4 x +c\)

b.  \(\frac{1}{4}\sin^4 x +c\)

c.  \(\cos x - \frac{1}{3} \cos^3 x + c\)

d.  \(\sin x - \frac{1}{3} \sin^3 x + c\)

e.  \(3\cos^2 x \sin x + c\)

 

2. \(\int \cos^5 x dx \)

a.  \(\frac{1}{6}\cos^6 x +c\)

b.  \(\frac{1}{6}\sin^6 x +c\)

c.  \(\sin x - \frac{2}{3}\sin^3 x +\frac{1}{5} \sin^5 x + c\)

d.  \(\sin x - \frac{1}{3}\sin^3 x +\frac{2}{5} \sin^5 x + c\)

e.  \(5\cos^4 x \sin x + c\)

 

3. \(\int \cos^6 x dx \)

a.  \(\frac{5}{16}x + \frac{1}{4}\sin 2x + \frac{3}{64} \sin 4x - \frac{1}{48} \sin^3 2x + c\)

b.  \(\frac{5}{16}x + \frac{15}{64}\sin 2x + \frac{3}{64} \sin 4x - \frac{1}{192} \sin^3 2x + c\)

c.  \(\frac{5}{16}x + \frac{17}{64}\sin 2x + \frac{3}{64} \sin 4x - \frac{1}{192} \sin^3 2x + c\)

d.  \(\frac{5}{16}x + \frac{15}{64}\sin 2x + \frac{3}{64} \sin 4x - \frac{1}{96} \sin^3 2x + c\)

e.  \(\frac{5}{16}x + \frac{17}{64}\sin 2x + \frac{3}{64} \sin 4x - \frac{1}{96} \sin^3 2x + c\)

 

4. \(\int \cos^2 2x dx \)

a.  \(\frac{x}{2} +\frac{1}{8}\sin(4x) +c\)

b.  \(\frac{x}{8} +\frac{1}{4}\sin(4x) +c\)

c.  \(\frac{x}{8} +\frac{1}{8}\sin(4x) +c\)

d.  \(\frac{1}{3}\sin^3 2x + c\)

e.  \(\frac{1}{6}\sin^3 2x + c\)

 

5. \(\int \sec^4 x dx \)

a.  \(\frac{1}{5}\sec^5 x +c\)

b.  \(\frac{1}{5}\cos^5 x +c\)

c.  \(\frac{1}{5}\tan^5 x + \tan x +c\)

d.  \(\frac{1}{3}\tan^3 x + \tan x +c\)

e.  \(\frac{1}{6}\sec^6 x + \sec x + c\)

 

6. \(\int \sec x \tan^3 x dx \)

a.  \(\frac{1}{3}\sec^3 x +c\)

b.  \(\frac{1}{3}\tan^3 x +c\)

c.  \(\frac{1}{3}\sec^3 x - \sec x +c\)

d.  \(\frac{1}{3}\sec^3 x + \sec x +c\)

e.  \(\frac{1}{3}\tan^3 x + \tan x +c\)

 

7. \(\int x^3\sqrt{1-x^2} dx \)

a.  \(\frac{1}{5}(\sqrt{1-x^2})^5 + \frac{1}{3}(\sqrt{1-x^2})^3 +c\)

b.  \(\frac{1}{5}(\sqrt{1-x^2})^5 - \frac{1}{3}(\sqrt{1-x^2})^3 +c\)

c.  \(\frac{1}{4}(\sqrt{1-x^2})^4 + \frac{1}{2}(\sqrt{1-x^2})^2 +c\)

d.  \(\frac{1}{4}(\sqrt{1-x^2})^4 - \frac{1}{2}(\sqrt{1-x^2})^2 +c\)

e.  \(\frac{1}{6}x^4 \sqrt{1-x^2}^3 +c\)