   Chapter 8.7, Problem 55E

Chapter
Section
Textbook Problem

Finding or Evaluating an Integral In Exercises 55–62, find or evaluate the integral. ∫ 1 2 − 3 sin θ   d θ

To determine

To calculate: The value of the indefinite integral 123sinθdθ by the use of a table of integrals.

Explanation

Given:

The integral is: 123sinθdθ.

Formula used:

Use the formula 24 from the table of integrals:

1u2a2du=12aln|uau+a|+C

Calculation:

Consider the provided integral,

123sinθdθ

Let u=tanθ2.

Then du=2sec2θ2dθ.

And

sinθ=2u1+u2sec2θ2=11+u2

Now, substitute the values in the provided integral.

123sinθdθ=2du1+u223(2u1+u2)=22(1+u2)6udu=1u23u+1du=1(u32)254du

Now, use the formula 24

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