적분 기법 전체 문제

Use a table of integrals to evaluate the following integrals.

$\int \frac{1}{4{x}^{2}+25}dx$

Use a table of integrals to evaluate the following integrals.

$\int \frac{dy}{\sqrt{4-{y}^{2}}}$

Use a table of integrals to evaluate the following integrals.

$\int {\sin }^{3}(2x)\cos (2x)dx$

Use a table of integrals to evaluate the following integrals.

$\int \csc (2w)\cot (2w)dw$

Use a table of integrals to evaluate the following integrals.

$\int {2}^{y}dy$

Use a table of integrals to evaluate the following integrals.

${\int }_{0}^{1}\frac{3xdx}{\sqrt{{x}^{2}+8}}$

Use a table of integrals to evaluate the following integrals.

${\int }_{-1/4}^{1/4}{\sec }^{2}(\pi x)\tan (\pi x)dx$

Use a table of integrals to evaluate the following integrals.

${\int }_{0}^{\pi /2}{\tan }^{2}\left(\frac{x}{2}\right)dx$

Use a table of integrals to evaluate the following integrals.

$\int {\cos }^{3}xdx$

Use a table of integrals to evaluate the following integrals.

$\int {\tan }^{5}(3x)dx$

Use a table of integrals to evaluate the following integrals.

$\int {\sin }^{2}y{\cos }^{3}ydy$

Use tables to evaluate the integrals. You may need to complete the square or change variables to put the integral into a form given in the table.

$\int \frac{dx}{{x}^{2}+2x+10}$

Use tables to evaluate the integrals. You may need to complete the square or change variables to put the integral into a form given in the table.

$\int \frac{dx}{\sqrt{{x}^{2}-6x}}$

Use tables to evaluate the integrals. You may need to complete the square or change variables to put the integral into a form given in the table.

$\int \frac{{e}^{x}}{\sqrt{{e}^{2x}-4}}dx$

Use tables to evaluate the integrals. You may need to complete the square or change variables to put the integral into a form given in the table.

$\int \frac{\cos x}{{\sin }^{2}x+2\sin x}dx$

Use tables to evaluate the integrals. You may need to complete the square or change variables to put the integral into a form given in the table.

$\int \frac{\arctan ({x}^{3})}{{x}^{4}}dx$

Use tables to evaluate the integrals. You may need to complete the square or change variables to put the integral into a form given in the table.

$\int \frac{\ln |x|\arcsin (\ln |x|)}{x}dx$

Find the area bounded by $y=\frac{5}{4+25{x}^{2}},x=0,y=0,\text{and}\,x=4.$ Use a table of integrals or a CAS.

The region bounded between the curve $y=\frac{1}{\sqrt{1+\cos x}},0.3\le x\le 1.1,$ and the x-axis is revolved about the x-axis to generate a solid. Use a table of integrals to find the volume of the solid generated. (Round the answer to two decimal places.)

Use substitution and a table of integrals to find the area of the surface generated by revolving the curve $y={e}^{x},0\le x\le 3,$ about the x-axis. (Round the answer to two decimal places.)