Match List-I with List-II | List-I | List-II | | --- | --- | | (A) The value of $\int_{0}^{4} \vert x\vert \, dx$ is | (I) 3 | | (B) The value of $\int_{-2}^{2} \vert x\vert \, dx$ is | (II) -1 | | (C) The value of $\int_{0}^{3} [x] \, dx$ is | (III) 8 | | (D) The value of $\int_{-1}^{1} [x] \, dx$ is | (IV) 4 | Choose the correct answer from the options given below:

If $0 < x < \frac{\pi}{4}$, then $\int\sqrt{1-\sin2x}\,dx$ is:

[where C is an arbitrary constant]

$\int e^x \left(\frac{1}{x} - \frac{2}{x^3}\right) dx =$

$\int_{4}^{10} \frac{\log(x^2)}{\log(x^2)+\log(196-28x+x^2)}dx$ is equal to : (Consider $\log_e x = \log x$)

The value of $\int_{-1}^{1} \dfrac{x^6}{6^x+1}\,dx$ is

The value of the definite integral $I = \int_{1}^{2} \frac{1}{x(1 + x^2)}dx$ is:

$\int \frac{x^2+1}{(x+1)^2} e^x \, dx$ is equal to