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(c) \int_0^1 \tan(\pi x) dx Since the function y = \tan(\pi x) has an infinite discontinuity at x = 0, the integral is a Type 2 improper integral. Since the function y = \tan(\pi x) has an infinite discontinuity at x = \frac{1}{2}, the integral is a Type 2 improper integral. Since the function y = \tan(\pi x) has an infinite discontinuity at x = 1, the integral is a Type 2 improper integral. Since the integral \int_0^1 \tan(\pi x) dx has an infinite interval of integration, it is a Type 1 improper integral. Since the integral \int_0^1 \tan(\pi x) dx has an infinite interval of integration, it is a Type 2 improper integral.

          (c) \int_0^1 \tan(\pi x) dx
Since the function y = \tan(\pi x) has an infinite discontinuity at x = 0, the integral is a Type 2 improper integral.
Since the function y = \tan(\pi x) has an infinite discontinuity at x = \frac{1}{2}, the integral is a Type 2 improper integral.
Since the function y = \tan(\pi x) has an infinite discontinuity at x = 1, the integral is a Type 2 improper integral.
Since the integral \int_0^1 \tan(\pi x) dx has an infinite interval of integration, it is a Type 1 improper integral.
Since the integral \int_0^1 \tan(\pi x) dx has an infinite interval of integration, it is a Type 2 improper integral.

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(c) ∫0^1 tan(πx) dx
Since the function y = tan(πx) has an infinite discontinuity at x = 0, the integral is a Type 2 improper integral.
Since the function y = tan(πx) has an infinite discontinuity at x = (1)/(2), the integral is a Type 2 improper integral.
Since the function y = tan(πx) has an infinite discontinuity at x = 1, the integral is a Type 2 improper integral.
Since the integral ∫0^1 tan(πx) dx has an infinite interval of integration, it is a Type 1 improper integral.
Since the integral ∫0^1 tan(πx) dx has an infinite interval of integration, it is a Type 2 improper integral.

Added by Alejandro W.

Calculus: Early Transcendentals

James Stewart 8th Edition

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Solved by Expert Lucas Finney

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Step 1: State the integral: I = ∫_0^1 tan(pi x) dx. Show more…

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(c) int_0^1 tan(pi x)dx Since the function y=tan(pi x) has an infinite discontinuity at x=0, the integral is a Type 2 improper integral. Since the function y=tan(pi x) has an infinite discontinuity at x=(1)/(2), the integral is a Type 2 improper integral. Since the function y=tan(pi x) has an infinite discontinuity at x=1, the integral is a Type 2 improper integral. Since the integral int_0^1 tan(pi x)dx has an infinite interval of integration, it is a Type 1 improper integral. Since the integral int_0^1 tan(pi x)dx has an infinite interval of integration, it is a Type 2 improper integral. (c) tan(xdx Since the function y= tan(x has an infinite discontinuity at x=0,the integral is a Type 2 improper integral Since the function y= tanx has an infinite discontinuity at x=1,the integral is a Type 2 improper integral. O Since the integral tan(x) dx has an infinite interval of integration, it is a Type 1 improper integral. O Since the integral tan(x dx has an infinite interval of integration, it is a Type 2 improper integral.

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