Chapter 11

Find the indefinite integral. $$\int x^{2}\left(2 x^{3}+3\right)^{4} d x$$

Find the indefinite integral. $$\int \sqrt{2} d x$$

Find the amount of an annuity if $$\$ 250 /$$ month is paid into it for a period of \(20 \mathrm{yr}\), earning interest at the rate of \(8 \% / y\) ear compounded continuously.

Sketch the graph and find the area of the region bounded below by the graph of each function and above by the \(x\) -axis from \(x=a\) to \(x=b\). $$f(x)=x^{2}-5 x+4 ; a=1, b=3$$

Evaluate the definite integral. $$\int_{-1}^{1} x^{2}\left(x^{3}+1\right)^{4} d x$$

Find the area of the region under the graph of the function \(f\) on the interval \([a, b]\). $$f(x)=\sqrt{x} ;[1,9]$$

Find the indefinite integral. $$\int \frac{x^{4}}{1-x^{5}} d x$$

Find the indefinite integral. $$\int x^{3} d x$$

Find the amount of an annuity if $$\$ 400 /$$ month is paid into it for a period of \(20 \mathrm{yr}\), earning interest at the rate of \(6 \% / y\) ear compounded continuously.

Sketch the graph and find the area of the region bounded below by the graph of each function and above by the \(x\) -axis from \(x=a\) to \(x=b\). $$f(x)=x^{3} ; a=-1, b=0$$

Evaluate the definite integral. $$\int_{1}^{2}\left(x^{3}+\frac{3}{4}\right)\left(x^{4}+3 x\right)^{-2} d x$$

Find the area of the region under the graph of the function \(f\) on the interval \([a, b]\). $$f(x)=x^{3} ;[1,3]$$

Find the indefinite integral. $$\int \frac{x^{2}}{\sqrt{x^{3}-1}} d x$$

Find the indefinite integral. $$\int 2 x^{5} d x$$

Aiso deposits $$\$ 150 /$$ month in a savings account paying \(6 \% /\) year compounded continuously. Estimate the amount that will be in his account after 15 yr.

Sketch the graph and find the area of the region bounded below by the graph of each function and above by the \(x\) -axis from \(x=a\) to \(x=b\). $$f(x)=-1-\sqrt{x} ; a=0, b=9$$

Evaluate the definite integral. $$\int_{1}^{5} x \sqrt{x-1} d x$$

Find the area of the region under the graph of the function \(f\) on the interval \([a, b]\). $$f(x)=1-\sqrt[3]{x} ;[-8,-1]$$

Find an approximation of the area of the region \(R\) under the graph of the function \(f\) on the interval \([a, b] .\) In each case, use \(n\) subintervals and choose the representative points as indicated. \(f(x)=x^{2}+1 ;[0,2] ; n=5 ;\) midpoints

Find the indefinite integral. $$\int \frac{2}{x-2} d x$$

Find the indefinite integral. $$\int x^{-4} d x$$

The Armstrongs wish to establish a custodial account to finance their children's education. If they deposit $$\$ 200$$monthly for 10 yr in a savings account paying \(6 \% /\) year compounded continuously, how much will their savings account be worth at the end of this period?

Sketch the graph and find the area of the region bounded below by the graph of each function and above by the \(x\) -axis from \(x=a\) to \(x=b\). $$f(x)=\frac{1}{2} x-\sqrt{x} ; a=0, b=4$$

Evaluate the definite integral. $$\int_{1}^{4} x \sqrt{x+1} d x$$

Find the area of the region under the graph of the function \(f\) on the interval \([a, b]\). $$f(x)=\frac{1}{\sqrt{x}} ;[1,9]$$

Find an approximation of the area of the region \(R\) under the graph of the function \(f\) on the interval \([a, b] .\) In each case, use \(n\) subintervals and choose the representative points as indicated. \(f(x)=4-x^{2} ;[-1,2] ; n=6 ;\) left endpoints

Find the indefinite integral. $$\int 3 t^{-7} d t$$

Sketch the graph and find the area of the region bounded below by the graph of each function and above by the \(x\) -axis from \(x=a\) to \(x=b\). $$f(x)=-e^{(1 / 2) x} ; a=-2, b=4$$

Evaluate the definite integral. $$\int_{0}^{2} x e^{x^{2}} d x$$

Find the area of the region under the graph of the function \(f\) on the interval \([a, b]\). $$f(x)=e^{x} ;[0,2]$$

Find an approximation of the area of the region \(R\) under the graph of the function \(f\) on the interval \([a, b] .\) In each case, use \(n\) subintervals and choose the representative points as indicated. \(f(x)=\frac{1}{x},[1,3] ; n=4 ;\) right endpoints

Find the indefinite integral. $$\int \frac{0.3 x-0.2}{0.3 x^{2}-0.4 x+2} d x$$

Find the indefinite integral. $$\int x^{2 / 3} d x$$

Sketch the graph and find the area of the region bounded below by the graph of each function and above by the \(x\) -axis from \(x=a\) to \(x=b\). $$f(x)=-x e^{-x^{2}} ; a=0, b=1$$

Evaluate the definite integral. $$\int_{0}^{1} e^{-x} d x$$

Find the area of the region under the graph of the function \(f\) on the interval \([a, b]\). $$f(x)=e^{x}-x ;[1,2]$$

Find an approximation of the area of the region \(R\) under the graph of the function \(f\) on the interval \([a, b] .\) In each case, use \(n\) subintervals and choose the representative points as indicated. \(f(x)=e^{x} ;[0,3] ; n=5 ;\) midpoints

Find the indefinite integral. $$\int \frac{2 x^{2}+1}{0.2 x^{3}+0.3 x} d x$$

Find the indefinite integral. $$\int 2 u^{3 / 4} d u$$

Estimate the present value of an annuity if payments are $$\$ 1200$$ monthly for \(15 \mathrm{yr}\) and the account earns interest at the rate of \(6 \% /\) year compounded continuously.

Sketch the graphs of the functions \(f\) and \(g\) and find the area of the region enclosed by these graphs and the vertical lines \(x=a\) and \(x=b\). $$f(x)=x^{2}+3, g(x)=1 ; a=1, b=3$$

Evaluate the definite integral. $$\int_{0}^{1}\left(e^{2 x}+x^{2}+1\right) d x$$

Evaluate the definite integral. $$\int_{2}^{4} 3 d x$$

Find the indefinite integral. $$\int \frac{x}{3 x^{2}-1} d x$$

Find the indefinite integral. $$\int x^{-5 / 4} d x$$

A state lottery commission pays the winner of the "Million Dollar" lottery 20 annual installments of $$\$ 50,000$$ each. If the prevailing interest rate is \(6 \% /\) year compounded continuously, find the present value of the winning ticket.

Sketch the graphs of the functions \(f\) and \(g\) and find the area of the region enclosed by these graphs and the vertical lines \(x=a\) and \(x=b\). $$f(x)=x+2, g(x)=x^{2}-4 ; a=-1, b=2$$

Evaluate the definite integral. $$\int_{0}^{2}\left(e^{t}-e^{-t}\right) d t$$

Evaluate the definite integral. $$\int_{-1}^{2}-2 d x$$

Find the indefinite integral. $$\int \frac{x^{2}-1}{x^{3}-3 x+1} d x$$