Identify which method to use integrating?

Question

http://fog.ccsf.cc.ca.us/~wjeh/math110B/calculus2_exercise_methods_of_integration_answers.pdf

From 5a. to 5n. WHICH methods of integration would you use? (integration by parts, trig sub, u sub, etc.,) I seem to be lost when it comes to starting out an integral. Suggestions?

Thanks :)

匿名 · Accepted Answer

For most part, you need to use substitution method.  For definite integrals, you need to apply FTC (First Fundamental Theorem of Calculus).

a. Note that the expression is same as sin(x)/cos(x) * sin²(x) = tan(x)(1 - cos²(x)) = tan(x) - sin(x)cos(x).  Then, let u = cos(x)
b. Use substitution method.  Let u = x² and du = 2x dx.  Then, use trigonometric integral.
c. Use substitution method again.
d. Like part (b)
e. Let u = ln(x) and du = 1/x dx.
f. Integrate by parts
g. Let u = x³ - 2x - 8 and du = 3x² - 2 dx
h. Let u = 2x and du = 2 dx.
i. Use trigonometric identity sin(x) cos(y) = 1/2 (sin(x-y)+sin(x+y))
j. Let u = e^(x) and du = e^x dx
k. Integrate by parts.  Then, use substitution method.

You determine the last three parts by yourself.

I hope this helps!

? · Answer

that's 2 applications with trigs. The trick is once you have a sine and cosine function multiply jointly and the two of their powers are atypical, you ought to use u = cos(2x) or u = sin(2x), this is not proper.

Identify which method to use integrating?

2 個解答