CBSE 12 Mathematics Integrals MPQs
2. Find the following integrals:
- \(\int cos2xdx\)
- \(\int (4e^{3x}+1)dx\)
- \(\int (\sqrt{x}-\frac{1}{\sqrt x})^2dx\)
- \(\int \frac{x^3 - x^2 +x - 1}{x-1}dx\)
- \(\int (\sqrt{x}(3x^2 + 2x +3)dx\)
- \(\int secx(secx+tanx)dx\)
- \(\int (\frac{sec^2x}{cosec^2x})dx\)
- \(\int (\frac{2-3x}{cos^2{x}})^2dx\)
3. Integrate the following functions:
- \(\frac{2x}{1+x^2}\)
- \(\frac{(logx)^2}{x}\)
- \(\frac{1}{x-\sqrt x}\)
- \(\frac{e^{2x}-1}{e^{2x}+1}\)
- \(\frac{e^{2x}-e^{-2x}}{e^{2x}+e^{-2x}}\)
- \(\frac{(1+logx)^2}{x}\)
- \(\frac{(x+1)(x+logx)^2}{x}\)
- \(\frac{cosx}{\sqrt{1+sinx}}\)
4. Integrate the following rational functions:
- \(\frac{x}{(x+1)(x+2)}\)
- \(\frac{x}{(x+1)(x+2)(x+3)}\)
- \(\frac{cosx}{(1-sinx)(2-sinx)}\)
- \(\frac{3x-1}{(x+2)^2}\)
- \(\frac{1}{x^4 -1{}}\)
- \(\frac{x^3 + x + 1}{x^2 - 1}\)
- \(\frac{1}{x(x^n + 1)}\)
- \(\frac{3x+5}{x^3 - x^2}\)
5. Evaluate the following integrals:
- \(\int_0^1 \frac{x}{x^2+1}dx\)
- \(\int_{-1}^1 {(x+1)}dx\)
- \(\int_3^2 \frac{1}{x}dx\)
- \(\int_0^{\pi/4} tanx dx\)
- \(\int_0^{\pi/4} (2sec^2x+x^3+2) dx\)
- \(\int_0^{\pi/4} sin2x dx\)
- \(\int_0^{\pi/4} (sin^2\frac{x}{2}- cos^2 \frac{x}{2}) dx\)
- \(\int_0^{\pi/4} sin2x dx\)
- \(\int_2^3 \frac{dx}{x^2-1}\)
6. Evaluate the integral: $$\int x^2 \, dx$$
7. Find the area under the curve: $$y = x^3$$ from x = 0 to x = 2.
8. Solve: $$\int (3x^2 + 2x + 1) \, dx$$
9. Evaluate: $$\int \sin(x) \, dx$$
10. Find the value of: $$\int e^x \, dx$$
11. Solve the integral: $$\int \frac{1}{x} \, dx$$
12. Evaluate: $$\int \cos(x) \, dx$$
13. Find the integral of the function: $$\int (x^3 - 4x + 6) \, dx$$
14. Determine the integral: $$\int \frac{1}{x^2} \, dx$$
15. Evaluate the definite integral: $$\int_0^1 (2x^3 + x^2) \, dx$$