_(1/3)^1 ((x-x^3)^(1/3))/x^4 dx equals Option 1: 16/3 Option 2: 8 Option 3: 6 Option 4: 15/2

Answer: 6. Solution: Write (x-x^3)^(1/3)=x(1/x^2-1)^(1/3), so the integrand becomes 1/x^3(1/x^2-1)^(1/3). Put u=1/x^2-1, so du=-2/x^3dx; limits go from u=8 to u=0. Integral =12_0^8 u^(1/3)du=12348^(4/3)=38x16=6.

Calculus

Integrals

Hard

applied

$\int_{1/3}^{1} \frac{(x-x^3)^{1/3}}{x^4} dx$ equals

$\frac{16}{3}$

$\frac{15}{2}$

✅ Correct Option: 3

Write $(x-x^3)^{1/3}=x\left(\frac{1}{x^2}-1\right)^{1/3}$ , so the integrand becomes $\frac{1}{x^3}\left(\frac{1}{x^2}-1\right)^{1/3}$ .

Put $u=\frac{1}{x^2}-1$ , so $du=-\frac{2}{x^3}dx$ ; limits go from $u=8$ to $u=0$ .

Integral $=\frac12\int_0^8 u^{1/3}du=\frac12\cdot\frac34\cdot8^{4/3}=\frac38\times16=6$ .

2026: 30 May Shift 1

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

2025: 14 May Shift 1

$\int_1^4 |x - 2|dx$ is equal to

2025: 2 June Shift 1

The value of $\int_{-\pi/2}^{\pi/2}(x^5 + x^3\cos x)dx$ is

2025: 14 May Shift 2

$\int_{-1}^{1}(x^7 + x^5 + x^3 + x + 1)dx$ is equal to

2025: 30 May Shift 1

$\int_2^5 |x - 3|dx$ equals

2026: 29 May Shift 2

$\int_1^2 \frac{dx}{(x+1)(x+2)} =$

∫1/31(x−x3)1/3x4dx\int_{1/3}^{1} \frac{(x-x^3)^{1/3}}{x^4} dx∫1/31​x4(x−x3)1/3​dx equals

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

$\int_{1/3}^{1} \frac{(x-x^3)^{1/3}}{x^4} dx$ equals