CPM Homework Help : CALC Problem 5-72

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5-72.

Evaluate the following integrals without a calculator.

$\int _ { - 1 } ^ { - 1 } ( - 9 t ^ { 6 / 5 } - 15 t ^ { - 11 / 3 } ) d t$
Hint (a):
Fundamental Theorem of Calculus, Part 1.

$\int _ { 0 } ^ { 2 } \frac { d } { d x } ( 9 x - 1 ) d x$
Hint (b):
Fundamental Theorem of Calculus, Part 1.

$\int ( - 32 t + 12 ) d t$
Answer (c):
$−16t^2 + 12t + C$

$\int \operatorname { cos } ( 5 x ) d x$
Hint (d):
$k\operatorname{ sin}(5x) + C$ . Find k.

$\int _ { 1 } ^ { - 1 } ( 4 x ^ { 2 } - 6 x ) d x + \int _ { 1 } ^ { 2 } ( 2 x ^ { 2 } - 3 x ) d x$
Answer (e):
$\frac{4}{3}x^3-3x^2\Big|_1^{-1}-\frac{2}{3}x^3-\frac{3}{2}x^2\Big|_1^2=-\frac{7}{3}$

Compute without a calculator

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