Question 330-335 of 346: Integration and Its Applications (Section A: Common) | CUET (Common University Entrance Test) UG Mathematics Common (319) | Includes PYQs | Get Solutions with Detailed Explanations

The value of ${\displaystyle \underset{-\frac{\pi }{2}}{\overset{\frac{\pi }{2}}{\int }}\frac{\mathrm{d}x}{\left[x\right]+\left[\sin x\right]+4}}$ , where [t] denotes the greatest integer less than or equal to t, is: (January Shift 2)

The area (in sq. units) of the region bounded by the curve x² = 4 y and the straight line ${\displaystyle x=4y-2}$ is: (January Shift 1)

The value of the integral ${\displaystyle \underset{-2}{\overset{2}{\int }}\frac{si{n}^{2}x}{\left[\frac{x}{\pi }\right]+\frac{1}{2}}\mathrm{d}x}$ (where [x] denotes the greatest integer less than or equal to x) is: (January Shift 1)

If ${\displaystyle \int \frac{\sqrt{1-x^2}}{x^4}\mathrm{d}x=A\left(x\right){\left(\sqrt{1-x^2}\right)}^m+C}$ , for a suitable chosen integer m and a function A (x), where C is a constant of integration, then (A (x) )^m equals: (January Shift 1)

If ${\displaystyle \int \frac{x+1}{\sqrt{2x-1}}\mathrm{d}x=f\left(x\right)\sqrt{2x-1}+C}$ , where C is a constant of integration, then f (x) is equal to: (January Shift 2)

The area (in sq. units) in the first quadrant bounded by the parabola, y = x² + 1, the tangent to it at the point (2,5) and the coordinate axes is: (January Shift 2)