27. Let f(x) = x2(x3 + 1)4. What is the area under the graph of f over the closed interval [-1,1]?
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A. 0 |
B. 32/15 |
C. 62/15 |
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D. 64/15 |
E. 32/5 |
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Solution: The answer is B
The area under the graph of f over the closed interval [-1,1] can be obtained by integrating f(x) with respect to x over the interval [-1,1]. That is, solve the following integral,
Use the method of variable substitution, by letting u = x3 + 1, so that,
