Recent questions tagged definite-integral

The Fourier cosine series of a function is given by : $$f\left ( x \right ) = \sum_{n = 0}^{\infty} f_{n} \cos nx$$ For $f\left ( x \right ) = \cos^{4} x$, the numerical ...

The value ($\textit{round off to one decimal place}$) of $\int_{-1}^{1}x\:e^{\left | x \right |}dx$ is ______________

Consider the following definite integral: $I= \displaystyle{} \int_0^1 \dfrac{(\sin ^{-1}x)^2}{\sqrt{1-x^2}} dx$. The value of the integral is$\dfrac{\pi ^3}{24} \\$$\dfr...

The area between the parabola $x^2=8y$ and the straight line $y=8$ is _______.

The value of $\int_0^{\infty} \dfrac{1}{1+x^2} dx + \int _0^{\infty} \dfrac{\sin x}{x} dx$ is$\dfrac{\pi}{2} \\$$\pi \\$$\dfrac{3 \pi}{2} \\$$1$

The area of the region bounded by the parabola $y=x^2+1$ and the straight line $x+y=3$ is$\dfrac{59}{6} \\$$\dfrac{9}{2} \\$$\dfrac{10}{3} \\$$\dfrac{7}{6}$

Given, $i=\sqrt{-1}$, the value of the definite integral, $I= \int_0^{\pi/2} \dfrac{\cos x+ i \sin x}{\cos x – i \sin x} dx$ is:$1$$-1$$i$$-i$

The solution for $\int_0^{\pi/6} \cos^4 3 \theta \sin^3 6 \theta \: d \theta$ isA. $0$B. $\dfrac{1}{15}$C. $1$D. $\dfrac{8}{3}$

The value of the integral $\int_0^{\pi} x \cos^2 x \: dx$ is$\pi^2/8$$\pi^2/4$$\pi^2/2$$\pi^2$