_1^3 √x/(√x+√(4-x))dx is equal to: Option 1: -1 Option 2: 2 Option 3: 1 Option 4: 0

Answer: 1. Solution: Use the property _a^b f(x)dx = _a^b f(a+b-x)dx with a+b = 4. This gives I = _1^3 (√(4-x))/(√(4-x)+√x)dx. Adding the two forms, 2I = _1^3 1 dx = 2, so I = 1.

Calculus

Integrals

Medium

core

$\displaystyle\int_1^3 \dfrac{\sqrt{x}}{\sqrt{x}+\sqrt{4-x}}dx$ is equal to:

-1

✅ Correct Option: 3

Use the property $\int_a^b f(x)dx = \int_a^b f(a+b-x)dx$ with $a+b = 4$ .

This gives $I = \int_1^3 \dfrac{\sqrt{4-x}}{\sqrt{4-x}+\sqrt{x}}dx$ .

Adding the two forms, $2I = \int_1^3 1\,dx = 2$ , so $I = 1$ .

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∫13xx+4−xdx\displaystyle\int_1^3 \dfrac{\sqrt{x}}{\sqrt{x}+\sqrt{4-x}}dx∫13​x​+4−x​x​​dx is equal to:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

$\displaystyle\int_1^3 \dfrac{\sqrt{x}}{\sqrt{x}+\sqrt{4-x}}dx$ is equal to: