Questions from General Calculus


Q: Evaluate the integral by completing the square and using Formula 6.

Evaluate the integral by completing the square and using Formula 6.

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Q: Evaluate the integral by completing the square and using Formula 6.

Evaluate the integral by completing the square and using Formula 6.

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Q: The German mathematician Karl Weierstrass (1815–1897) noticed that

The German mathematician Karl Weierstrass (1815–1897) noticed that the substitution t = tan(x/2) will convert any rational function of sin x and cos x into an ordinary rational funct...

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Q: Use the substitution to transform the integrand into a rational function of

Use the substitution to transform the integrand into a rational function of t and then evaluate the integral.

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Q: Use the substitution to transform the integrand into a rational function of

Use the substitution to transform the integrand into a rational function of t and then evaluate the integral.

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Q: Use the substitution to transform the integrand into a rational function of

Use the substitution to transform the integrand into a rational function of t and then evaluate the integral.

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Q: Use the substitution to transform the integrand into a rational function of

Use the substitution to transform the integrand into a rational function of t and then evaluate the integral.

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Q: Find the area of the region under the given curve from 1

Find the area of the region under the given curve from 1 to 2.

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Q: Find the area of the region under the given curve from 1

Find the area of the region under the given curve from 1 to 2.

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Q: Find the volume of the resulting solid if the region under the

Find the volume of the resulting solid if the region under the curve / is rotated about (a) the x-axis and (b) the y-axis.

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