Exam 9: Techniques of Integration

$\int _ { 1 } ^ { 3 }$ $\frac { 1 } { x }$ dx; n = 4 Enter just a real number rounded to two decimal places.

$\int _ { 0 } ^ { x }$ $\frac { 1 } { \sqrt { 4 x + 5 } }$ dx Enter your answer as just a reduced fraction or the word "divergent".

Approximate $\int _ { 0 } ^ { 1 } \sqrt { 1 + x ^ { 3 } }$ dx; n = 4, by (a) Simpson's rule and (b) the trapezoidal rule. Enter your answers in that order as just unlabeled real numbers rounded to two decimal places, separated by a comma.

Approximate $\int _ { 1 } ^ { 3 } \frac { 1 } { x }$ dx; n = 10, by (a) Simpson's rule and (b) the trapezoidal rule. Enter your answers in that order as just unlabeled real numbers rounded to two decimal places, separated by commas.

$\int 2 \cos ^ { 2 } x \sin x d x$ Enter your answer with any coefficients in front as integers or reduced fractions of form $\frac { a } { b }$ .

Evaluate the integral. - $\int _ { 1 } ^ { 2 } 3 t$ dt

Does this integral $\int x ^ { 2 } e ^ { x } d x$ = $x ^ { 2 }$ $e ^ { x }$ - 2( $x e ^ { x }$ - $e ^ { x }$ ) + C?

$\int _ { 1 } ^ { 3 }$ $\frac { 1 } { x }$ dx; n = 4 Enter just a real number rounded to two decimal places.

$\int$ $\frac { ( \ln x ) ^ { 5 } } { x }$ dx Enter your answer with any coefficients in front as integers or reduced fractions of form a/b.

Determine the integral by making an appropriate substitution. - $\int \frac { \sec ^ { 2 } x } { ( 1 - 3 \tan x ) ^ { 1 / 2 } }$ dx

Does this integral $\int$ $\frac { x e ^ { - x } } { ( x - 1 ) ^ { 2 } }$ dx = $\frac { e ^ { - x } } { 1 - x }$ + C?

Evaluate the integral using integration by parts. - $\int e ^ { 2 x } \sin 3 x d x$

The following data give the marginal cost for different levels of production at Zipperty-Doo-Dah Inc. Here x represents the number of zippers produced and C'(x) is in dollars per zipper. Approximate the total in going from a production level of 50 zippers to 90 zippers. x 50 60 70 80 90 () 4.5 5.0 5.3 5.8 6.5

Does this integral $\int ( x + 2 ) \sin 2 x d x$ = $\frac { 1 } { 4 }$ sin 2x - $\frac { ( x + 2 ) } { 2 }$ cos 2x?

$\int x \left( x ^ { 2 } - 1 \right) ^ { 3 } d x$ Enter your answer with any coefficients in front as integers or reduced fractions of form a/b.

$\int \cos x \sin ^ { 2 } x d x$ Enter your answer with any coefficients in front as integers or reduced fractions of form $\frac { a } { b }$ . No parentheses around arguments of functions.

Evaluate the improper integral whenever it is convergent. If it is divergent, state this. - $\int _ { 1 } ^ { \infty } \frac { d x } { x }$

Evaluate the integral using integration by parts. - $\int x e ^ { 8 x }$ dx

Evaluate the integral. - $\int _ { 1 } ^ { 2 } \ln x d x$

$\int _ { 0 } ^ { x }$ $\frac { ( x + 1 ) } { ( x + 1 ) ^ { 3 } }$ dx Enter your answer as an integer or the word "divergent".