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Homework for Chapter 7.3: Trigonometric Substitutions
#38
Question A:
i) Graph 1/sqrt(1-x^2)
ii) Find the integral of 1/sqrt(1-x^2) dx by using the substitution
x = cos(theta)
iii) Graph your answer to (ii) and visually check that its derivative
is 1/sqrt(1-x^2).
If the graph of part (i) doesn't look like the deriv. of your
answer to part (ii), redo part (ii) before going on!
iv) Check your answer by taking the derivative.
v) Explain how your answer compares to the one we found in class
(or the one in the integral table), which comes from using
x = sin(theta)
Question B:
i) Graph sqrt(1-x^2)
ii) Find the integral of sqrt(1-x^2) dx by using the substitution
x = cos(theta)
iii) Graph your answer to (ii) and visually check that its derivative
is sqrt(1-x^2).
If the graph of part (i) doesn't look like the deriv. of your
answer to part (ii), redo part (ii) before going on!
iv) Check your answer by taking the derivative.
It takes some work to
simplify it--be persistent.
v) Explain how your answer compares to the one we found in class

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