CBSE 12 Mathematics Integrals MPQs

CBSE 12 Mathematics Integrals MPQs

2. Find the following integrals:

1. \(\int cos2xdx\)
2. \(\int (4e^{3x}+1)dx\)
3. \(\int (\sqrt{x}-\frac{1}{\sqrt x})^2dx\)
4. \(\int \frac{x^3 - x^2 +x - 1}{x-1}dx\)
5. \(\int (\sqrt{x}(3x^2 + 2x +3)dx\)
6. \(\int secx(secx+tanx)dx\)
7. \(\int (\frac{sec^2x}{cosec^2x})dx\)
8. \(\int (\frac{2-3x}{cos^2{x}})^2dx\)

3. Integrate the following functions:

1. \(\frac{2x}{1+x^2}\)
2. \(\frac{(logx)^2}{x}\)
3. \(\frac{1}{x-\sqrt x}\)
4. \(\frac{e^{2x}-1}{e^{2x}+1}\)
5. \(\frac{e^{2x}-e^{-2x}}{e^{2x}+e^{-2x}}\)
6. \(\frac{(1+logx)^2}{x}\)
7. \(\frac{(x+1)(x+logx)^2}{x}\)
8. \(\frac{cosx}{\sqrt{1+sinx}}\)

4. Integrate the following rational functions:

1. \(\frac{x}{(x+1)(x+2)}\)
2. \(\frac{x}{(x+1)(x+2)(x+3)}\)
3. \(\frac{cosx}{(1-sinx)(2-sinx)}\)
4. \(\frac{3x-1}{(x+2)^2}\)
5. \(\frac{1}{x^4 -1{}}\)
6. \(\frac{x^3 + x + 1}{x^2 - 1}\)
7. \(\frac{1}{x(x^n + 1)}\)
8. \(\frac{3x+5}{x^3 - x^2}\)

5. Evaluate the following integrals:

1. \(\int_0^1 \frac{x}{x^2+1}dx\)
2. \(\int_{-1}^1 {(x+1)}dx\)
3. \(\int_3^2 \frac{1}{x}dx\)
4. \(\int_0^{\pi/4} tanx dx\)
5. \(\int_0^{\pi/4} (2sec^2x+x^3+2) dx\)
6. \(\int_0^{\pi/4} sin2x dx\)
7. \(\int_0^{\pi/4} (sin^2\frac{x}{2}- cos^2 \frac{x}{2}) dx\)
8. \(\int_0^{\pi/4} sin2x dx\)
9. \(\int_2^3 \frac{dx}{x^2-1}\)