3. The following is an incorrect solution to evaluating the integral of dx/(1 + 4x^2)^3/2 . Set x = tan θ. Then the integral becomes: the integral of dx/(1 + 4x^2)^3/2 = integral of dθ^(1 + 4 tan2 θ)^3/2 = intgral of dθ/ (sec^2 θ)^3/2 =integral of dθ/sec^3 θ =intgral of cos^3θ dθ = integral of (1 − sin^2 θ) cos θ dθ =integral of (1 − u^2) du = u − u^3/3+ C = sin θ − sin^3 θ/3 + C *Use u = sin θ, du = cos θ dθ. (a) There are MULTIPLE errors in the above work. Identify them all. (b) Provide a correct solution to evaluating this integral.
3. The following is an incorrect solution to evaluating the integral of dx/(1 + 4x^2)^3/2 . Set x = tan θ. Then the integral becomes: the integral of dx/(1 + 4x^2)^3/2 = integral of dθ^(1 + 4 tan2 θ)^3/2 = intgral of dθ/ (sec^2 θ)^3/2 =integral of dθ/sec^3 θ =intgral of cos^3θ dθ = integral of (1 − sin^2 θ) cos θ dθ =integral of (1 − u^2) du = u − u^3/3+ C = sin θ − sin^3 θ/3 + C *Use u = sin θ, du = cos θ dθ. (a) There are MULTIPLE errors in the above work. Identify them all. (b) Provide a correct solution to evaluating this integral.
Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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3. The following is an incorrect solution to evaluating the
dx/(1 + 4x^2)^3/2
.
Set x = tan θ. Then the integral becomes:
the integral of dx/(1 + 4x^2)^3/2 = integral of dθ^(1 + 4 tan2 θ)^3/2
= intgral of dθ/ (sec^2 θ)^3/2
=integral of dθ/sec^3 θ
=intgral of cos^3θ dθ
= integral of (1 − sin^2 θ) cos θ dθ
=integral of (1 − u^2) du
= u − u^3/3+ C
= sin θ − sin^3 θ/3 + C
*Use u = sin θ, du = cos θ dθ.
(a) There are MULTIPLE errors in the above work. Identify them all.
(b) Provide a correct solution to evaluating this integral.
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