Integration Problems from Textbook for Mathematics Students, Assignments of Mathematics

A list of ten integration problems for students to solve using the integral table in the inside covers of their textbook. The problems involve integrating various functions, including trigonometric functions and logarithmic functions, and some involve limits as well. Useful for students in calculus or advanced mathematics courses who need practice with integration.

Typology: Assignments

Pre 2010

Uploaded on 08/31/2009

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Additional HW problems, due October 3, 2005
Do the following problems using the integral table in the inside covers of
the book.
1. Rsin6θ
2. R(x23) log(2x)dx
3. R(y23) log(2 + y)dy
4. Rdx
x2+4x+3
5. Rx3e3xdx
6. Rsin3(3u) cos3(3u)du
7. R(s+ 1)2s+ 11ds
8. Rt2+1
t2
1dt
9. Rre2r2cos(2r2)dr
10. R1
0sin(mπx) sin(nπx)dx where m6=n.
(Remark: integral # 10 is useful in Fourier analysis, where one learns to
express arbitrary periodic functions as sums of sin and cos functions.)
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Additional HW problems, due October 3, 2005

Do the following problems using the integral table in the inside covers of

the book.

sin

6 θ dθ

(x^2 − 3) log(2x) dx

(y^2 − 3) log(2 + y) dy

∫ (^) dx x^2 +4x+

x^3 e^3 x^ dx

sin

3 (3u) cos^3 (3u) du

(s + 1)

2 s + 1

ds

∫ (^) t (^2) + t^2 − 1 dt

re^2 r

2 cos(2r^2 ) dr

0 sin(mπx) sin(nπx)^ dx^ where^ m^6 =^ n.

(Remark: integral # 10 is useful in Fourier analysis, where one learns to

express arbitrary periodic functions as sums of sin and cos functions.)