Find \(\int_{-1}^1 \,7x^6 \,(x^7+8)dx\)(a) -386(b) –\(\frac{386}{3}\)(c) \(\frac{386}{3}\)(d) 386I have been asked this question in examination.The question is from Evaluation of Definite Integrals by Substitution in section Integrals of Mathematics – Class 12

Find \(\int_{-1}^1 \,7x^6 \,(x^7+8)dx\)(a) -386(b) –\(\frac{386}{3}\

1.	Find \(\int_{-1}^1 \,7x^6 \,(x^7+8)dx\)(a) -386(b) –\(\frac{386}{3}\)(c) \(\frac{386}{3}\)(d) 386I have been asked this question in examination.The question is from Evaluation of Definite Integrals by Substitution in section Integrals of Mathematics – Class 12
Answer» CORRECT answer is (c) \(\frac{386}{3}\) For explanation I would say: I=\(\int_{-1}^1 \,7x^6 \,(X^7+8)DX\) Let x^7+8=t Differentiating w.r.t x, we get 7x^6 dx=dt The new limits When x=-1,t=7 When x=1,t=9 ∴\(\int_{-1}^1 \,7x^6 \,(x^7+8)dx=\int_7^9 \,t^2 \,dt\) =\([\frac{t^3}{3}]_7^9=\frac{1}{3} (9^3-7^3)=\frac{386}{3}\).

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Find \(\int_{-1}^1 \,7x^6 \,(x^7+8)dx\)(a) -386(b) –\(\frac{386}{3}\)(c) \(\frac{386}{3}\)(d) 386I have been asked this question in examination.The question is from Evaluation of Definite Integrals by Substitution in section Integrals of Mathematics – Class 12

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