The value of _0^3 √x/(√(3-x)+√x) dx is Option 1: 1/2 Option 2: 1 Option 3: 3/2 Option 4: 2

Answer: 3/2. Solution: Using _0^a f(x)dx = _0^a f(a-x)dx, call the integral I and add the transformed version: 2I = _0^3 1 dx = 3. Hence I = 3/2.

Calculus

Integrals

Medium

applied

The value of $\int_{0}^{3} \frac{\sqrt{x}}{\sqrt{3-x}+\sqrt{x}}\,dx$ is

$\frac{1}{2}$

$\frac{3}{2}$

✅ Correct Option: 3

Using $\int_0^a f(x)dx = \int_0^a f(a-x)dx$ , call the integral $I$ and add the transformed version: $2I = \int_0^3 1\,dx = 3$ . Hence $I = \frac{3}{2}$ .

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$\int_0^{\pi/2} \sqrt{1 - \sin 2x}\,dx$ is equal to:

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Match List I with List - II

List - I	List - II
A. An even function	I. $x^2 + \cos x$
B. For an even function, $\int_{-a}^{a} f(x)dx =$	II. 0
C. If $f(2a-x) = -f(x)$ , then $\int_{0}^{2a} f(x)dx =$	III. $2\int_{0}^{a} f(x)dx$
D. An odd function	IV. $x^3 + \sin x$

Choose the correct answer from the options given below:

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The value of $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} (\sin|x| + \cos|x|)dx$ , is equal to:

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The value of $\int_{-1}^{1}|x|dx$ is

The value of ∫03x3−x+x dx\int_{0}^{3} \frac{\sqrt{x}}{\sqrt{3-x}+\sqrt{x}}\,dx∫03​3−x​+x​x​​dx is

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The value of $\int_{0}^{3} \frac{\sqrt{x}}{\sqrt{3-x}+\sqrt{x}}\,dx$ is