Calculus

Integrals

Easy

core

$\displaystyle\int_{-\pi/3}^{\pi/3} 2x^5\cos^4 x\, dx$ equals

-1

✅ Correct Option: 1

$x^5$ is odd and $\cos^4x$ is even, so the integrand is odd.

Over the symmetric interval $[-\pi/3,\pi/3]$ the integral of an odd function is 0.

2025: 27 May Shift 1

The value of $\int_{-5}^{5} |x + 3| dx$ is

2026: 18 May Shift 2

If $f(x)=\int \sqrt{\dfrac{x+8}{x-8}}\,dx; f(8)=24\log_e 2$ , then $f(10)$ is equal to:

2022: 23 Aug Shift 1

$\int e^x \left(\frac{1}{x} - \frac{1}{x^2}\right) dx =$

2025: 15 May Shift 2

$\int \frac{(x^4 - x)^{1/4}}{x^5} dx$ is equal to

2025: 30 May Shift 2

$\int\limits_{\sqrt{log_e 2}}^{\sqrt{log_e 4}} xe^{x^2} dx$ is equal to

2026: 31 May Shift 2

The value of $\displaystyle\int_{\pi/6}^{\pi/3} \dfrac{\sin x+\cos x}{\sqrt{\sin 2x}}\,dx$ is:

∫−π/3π/32x5cos⁡4x dx\displaystyle\int_{-\pi/3}^{\pi/3} 2x^5\cos^4 x\, dx∫−π/3π/3​2x5cos4xdx equals