The three basic trigonometric substitutions are in the table below. Integral Contains Try using Substitution Va z = a sin 0, - <0< Va? +z2 * = a tan 0, z = a sec 0, 0<0< or <0 < Part 1. Using the substitution: ¤ = tan 0, – <<0 < , re-write the indefinite integral then evaluate in terms of 0. dr Note: type 'theta' for 0 and 'dtheta' for do. Part 2. Back substituting in the antiderivative you found in Part 1. above we have dz 1+x² Note: answer should be in terms of z only.

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A: Here we have to find the truth table.

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A: r(t)=8 cos7t i +8 sin7t j +3t kr'(t)=-56 sin7t i +56 cos7t j +3…

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A: Given: I=∫01e9ti+e-tj+tkdt As we know that; The Power rule: ∫xndx=xn+1n+1+C And ∫eax+bdx=1aeax+b+C

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A: We can find the answer as below using the given data.

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A: Alternating series test:∑n=0∞ (-1)nn+2an=(-1)nn+2bn=1n+2limn→∞1n+2 =0and bn+1-bn=1n+3-1n+2…

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