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dt

dt

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.5: The Binomial Theorem
Problem 47E
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Hi Can you please help me with this question? I am struggling with these definite integrals

dt and Include all working, Use calclos o Aind the definite ntegal
Transcribed Image Text:dt and Include all working, Use calclos o Aind the definite ntegal
Expert Solution
Step 1 : Analysis

Given :

∫014t2t3+1dt

Step 2 : Substitution

Let I = ∫014t2t3+1dt,

Substituting t3 + 1 = u,

Differentiating both sides with respect to t,

ddtt3 + 1 = dudt3t2 = dudt dt = du3t2

When t = 0 then u = 1

When t = 1 then u = 2

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