$\tan ^{-1}\left[\int_{-\pi / 2}^{\pi / 2} \frac{\cos x}{1+e^x} d x\right]=$

The absolute value of $\int_{10}^{19} \frac{\sin x}{1 + x^8} dx$ is less than:

If $\int_{-1}^{4} f(x) dx = 4$ and $\int_{2}^{4} (3 - f(x)) dx = 7$,then the value of $\int_{2}^{-1} f(x) dx$ is

Let $f : R \rightarrow R$ be a continuous function satisfying $f(x) + f(x + k) = n$,for all $x \in R$,where $k > 0$ and $n$ is a positive integer. If $I_{1} = \int_{0}^{4nk} f(x) dx$ and $I_{2} = \int_{-k}^{3k} f(x) dx$,then:

Let $f(x)$ be an even function with period $2$ and $f(x)$ be integrable on every interval. If $g(x) = \int_0^x f(t) dt$, then $g(x+2) =$

The value of $I = \int_{\pi / 2}^{5 \pi / 2} \frac{e^{\tan^{-1}(\sin x)}}{e^{\tan^{-1}(\sin x)} + e^{\tan^{-1}(\cos x)}} dx$ is