Topic
Q:
Evaluate the indefinite integral.
\( \int 8 \sin ^{3}(x) \cos (x) d x=\square+C \)
Q:
Integrate: \( \int 5 x \sqrt{x-2} d x \)
Q:
Integrate \( \int_{-2}^{2} 24(6 x-3)^{3} d x \)
Answer \( =\square \)
Q:
Evaluate the integral by making the given substitution.
\( \int \sec (4 x) \tan (4 x) d x, \quad u=4 x \)
\( +C \)
Q:
Evaluate the integral
\( \int x^{4}\left(x^{5}-7\right)^{8} d x \)
by making the substitution \( u=x^{5}-7 \).
Q:
\( \int _ { 0 } ^ { \frac { 1 } { 2 } } e ^ { x ^ { 2 } } = \)
Q:
Evaluate the integral
\( \int(2 x+5)\left(x^{2}+5 x+5\right)^{5} d x \)
by making the substitution \( u=x^{2}+5 x+5 \)
\( +C \)
Q:
Evaluate the integral
\( \int(2 x+5)\left(x^{2}+5 x+5\right)^{5} d x \)
by making the substitution \( u=x^{2}+5 x+5 \)
\( +C \)
Q:
Given the following two functions:
\[ f(x)=\frac{2 x}{x+1} \]
\[ g(x)=\frac{3 x-1}{x^{2}} \]
Find the limit of the product \( h(x)=f(x) \cdot g(x) \) as \( x \) approaches infinity.
Q:
A 25 -year old woman burns \( 350-70 t \mathrm{cal} / \mathrm{hr} \) while walking on her treadmill. Her caloric intake from
drinking Gatorade is \( 135 t \) calories during the \( t \) th hour. What is her net decrease in calories after walking
for 4 hours?
\( \square \)
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