Evaluate- -2 zdz - z 2-1A- None of these B- 3-2z4 - 3-cC- 3-2z2-1-2 - 3-cD- 3-2z2-12 - 3-c

The correct option is D Method 1.Let I = ∫2zdz/√(z^2+1) Let u=z^2+1, then du=2zdz I=∫ u^ 1/3du In the form of u^ndu = u^2/3/2/3+C Integrate with respect t ...

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Byju's Answer

Standard XII

Physics

Antiderivative

Evaluate: ∫2 ...

Question

Evaluate: $\int \frac{2zdz}{\sqrt[3]{z^2+1}}$

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None of these

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Solution

The correct option is B

Method-1.Let I = $\int \frac{2 z d z}{\sqrt[3]{z^{2} + 1}}$

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

$I = \int u^{- 1 / 3} d u$ In the form of $u^{n} d u$

= $\frac{u^{2 / 3}}{2 / 3} + C$ Integrate with respect to u.

= $\frac{3}{2} u^{2 / 3} + C = \frac{3}{2} (z^{2} + 1)^{2 / 3} + C$
( Replace u by $z^{2} + 1$ )

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Similar questions

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

Evaluate: $\int \frac{2 z d z}{\sqrt[3]{z^{2} + 1}}$

Q. Evaluate:

\int \frac{2 z d z}{\sqrt[3]{z^{2} + 1}}

Q. If

z_{1}, z_{2}, z_{3}, z_{4}

be the vertices of rhombus in argand palne and

∠ C B A = π / 3

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C o l u m n - I

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c o l u m n - I I

$C o l u m n - I$ (equation in z)	$C o l u m n - I I$ (principal value of arg(z))
$z^{2} - z + 1 = 0$	$- 2 π / 3$
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${2 z}^{2} + 1 - i \sqrt{3} = 0$	$2 π / 3$

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Evaluate: \(\int \frac{2zdz}{\sqrt[3]{z^2+1}}\)

The correct option is B Method-1.Let I = ∫2zdz3√z2+1 Let u=z2+1, then du=2zdz I=∫u−1/3du In the form of undu = u2/32/3+C Integrate with respect to u. = 32u2/3+C=32(z2+1)2/3+C ( Replace u by z2+1)