Problem 47
An acceleration function of an object moving along a straight line is given. Find the change of the object's velocity over the given time interval. $$ a(t)=-32 \mathrm{ft} / \mathrm{s}^{2} \text { on }[0,2] $$
Problem 48
An acceleration function of an object moving along a straight line is given. Find the change of the object's velocity over the given time interval. $$ a(t)=10 \mathrm{ft} / \mathrm{s}^{2} \text { on }[0,5] $$
Problem 49
An acceleration function of an object moving along a straight line is given. Find the change of the object's velocity over the given time interval. $$ a(t)=t \mathrm{ft} / \mathrm{s}^{2} \text { on }[0,2] $$
Problem 50
An acceleration function of an object moving along a straight line is given. Find the change of the object's velocity over the given time interval. $$ a(t)=\cos t \mathrm{ft} / \mathrm{s}^{2} \text { on }[0, \pi] $$
Problem 51
Sketch the given functions and find the area of the enclosed region. $$ y=2 x, y=5 x, \text { and } x=3 $$
Problem 52
Sketch the given functions and find the area of the enclosed region. $$ y=-x+1, y=3 x+6, x=2 \text { and } x=-1 $$
Problem 53
Sketch the given functions and find the area of the enclosed region. $$ y=x^{2}-2 x+5, y=5 x-5 $$
Problem 54
Sketch the given functions and find the area of the enclosed region. $$ y=2 x^{2}+2 x-5, y=x^{2}+3 x+7 $$
Problem 55
Find \(F^{\prime}(x)\). $$ F(x)=\int_{2}^{x^{3}+x} \frac{1}{t} d t $$
Problem 56
Find \(F^{\prime}(x)\). $$ F(x)=\int_{x^{3}}^{0} t^{3} d t $$
