Calculus

Integrals

Medium

applied

$I=\int_{2}^{8}\frac{\sqrt[3]{x+1}}{\sqrt[3]{x+1}+\sqrt[3]{11-x}}dx$ is equal to :

$\frac{1}{2}$

✅ Correct Option: 4

Here $a+b=2+8=10$ , and replacing $x$ by $10-x$ turns $x+1$ into $11-x$ , so $f(x)+f(10-x)=1$ .

Hence $2I=\int_2^8 1\,dx=6$ , giving $I=3$ .

2026: 12 May Shift 2

If $\displaystyle\int_0^{40} \dfrac{dx}{2x+1} = \log_e k$ , then the value of $k$ is :

2026: 18 May Shift 2

The value of $\int_{-1}^{1} \dfrac{x^6}{6^x+1}\,dx$ is

2025: 30 May Shift 2

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

2026: 29 May Shift 1

Match List-I with List-II

Choose the correct answer from the options given below:

2022: 30 Aug Shift 1

$\int \frac{xe^x}{(x+1)^2} dx =$

2025: 15 May Shift 2

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

I=∫28x+13x+13+11−x3dxI=\int_{2}^{8}\frac{\sqrt[3]{x+1}}{\sqrt[3]{x+1}+\sqrt[3]{11-x}}dxI=∫28​3x+1​+311−x​3x+1​​dx is equal to :