Evaluate -1- y 2 -2 ydyA- 2-31-y23-2-cB- 3-2y3-cC- 2-31-y2-cD- None of these

The correct option is A Let I= ∫√(1+y^2).2ydy Let u=1+y^2, then du=2ydy I=∫ u^1/2du=u^(1/2)+1/(1/2)+1Integrate, using rule no. 3 with n=1/2 = 2/3u^3/2+C Simp ...

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Byju's Answer

Standard XI

Mathematics

Infinite GP

Evaluate ∫√1+...

Question

Evaluate $\int \sqrt{1 + y^{2}} .2 y d y$

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None of these

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Solution

The correct option is A

Let $I = \int \sqrt{1 + y^{2}} .2 y d y$

Let $u = 1 + y^{2}$ , then $d u = 2 y d y$

$I = \int u^{1 / 2} d u = \frac{u^{(1 / 2) + 1}}{(1 / 2) + 1}$ Integrate, using rule no. 3 with n= $\frac{1}{2}$

= $\frac{2}{3} u^{3 / 2} + C$

Simpler form= $\frac{2}{3} (1 + y^{2})^{3 / 2} + c$ (Replace u by $1 + y^{2}$ )

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Evaluate ∫√1+y2.2ydy

The correct option is A Let I=∫√1+y2.2ydy Let u=1+y2, then du=2ydy I=∫u1/2du=u(1/2)+1(1/2)+1Integrate, using rule no. 3 with n=12 = 23u3/2+C Simpler form= 23(1+y2)3/2+c (Replace u by 1+y2)

Evaluate $\int \sqrt{1 + y^{2}} .2 y d y$