List of top Mathematics Questions on Some Properties of Definite Integrals asked in AP EAPCET

Evaluate $\int_{-\pi}^{\pi} \frac{\cos^2 x}{1+a^x} dx$

The value of the definite integral $\int_{-\pi/2}^{\pi/2} (x^3 + x\cos x + \tan^5 x + 1) \, dx$ is:

If \(f\) is a continuous function and \(f(x+T)=f(x), \forall x\in R\), it is given that \[ \int_0^{NT} f(t)\,dt=N\int_0^T f(t)\,dt \] \((N\) is a natural number). Then \[ \int_0^{50\pi}\sqrt{1-\cos 2x}\,dx= \]

Evaluate \[ \int_{-a}^{a} f(x)\,dx-\int_{0}^{a} f(-x)\,dx \]

Evaluate \[ \int_{-\pi}^{\pi}\frac{2x(1+\sin x)}{1+\cos^2x}\,dx \] is:

Evaluate \[ \int_{-1}^{1}\frac{\sin x-x^2}{3-|x|}\,dx = \]

Let \(T\gt 0\) be a fixed number. If \(f:\mathbb{R}\to\mathbb{R}\) is a continuous function such that \[ f(x+T)=f(x),\qquad x\in \mathbb{R}. \] If \[ I=\int_0^T f(x)\,dx, \] then \[ \int_0^{5T} f(2x)\,dx= \]