Indefinite Integrals - Maharashtra Board STD 12 Maths Questions

Q 1MCQ1 Mark

$\int\text{x}\sec\text{x}^2\text{ dx}$ is equal to:

✓
$\frac{1}{2}\log\big(\sec\text{x}^2+\tan\text{x}^2\big)+\text{C}$
B
$\frac{\text{x}^2}{2}\log\big(\sec\text{x}^2+\tan\text{x}^2\big)+\text{C}$
C
$2\log\big(\sec\text{x}^2+\tan\text{x}^2\big)+\text{C}$
D
none of these.

Answer: A.

View full solution →

Q 2MCQ1 Mark

The value of $\int\frac{1}{\text{x}+\text{x}\log\text{x}}\text{ dx}$ is:

A
$1+\log\text{x}$
B
$\text{x}+\log\text{x}$
C
$\text{x}\log\text{x}(1+\log\text{x})$
✓
$\log(1+\log\text{x})$

Answer: D.

View full solution →

Q 3MCQ1 Mark

$\int\frac{\text{x}+3}{(\text{x}+4)^2}\text{e}^{\text{x}}\text{ dx}=$

✓
$\frac{\text{e}^\text{x}}{\text{x}+4}+\text{C}$
B
$\frac{\text{e}^\text{x}}{\text{x}+3}+\text{C}$
C
$\frac{1}{(\text{x}+4)^2}+\text{C}$
D
$\frac{\text{e}^\text{x}}{(\text{x}+4)^2}+\text{C}$

Answer: A.

View full solution →

Q 4MCQ1 Mark

$\int\frac{1}{1-\cos\text{x}-\sin\text{x}}\text{ dx}=$

A
$\log\big|1+\cot\frac{\pi}{2}\big|+\text{C}$
B
$\log\big|1-\tan\frac{\pi}{2}\big|+\text{C}$
✓
$\log\big|1-\cot\frac{\pi}{2}\big|+\text{C}$
D
$\log\big|1+\tan\frac{\pi}{2}\big|+\text{C}$

Answer: C.

View full solution →

Q 5MCQ1 Mark

If $\int\frac{1}{(\text{x}+2)(\text{x}^2+1)}\text{ dx}=\text{a}\log|1+\text{x}^2|+\text{b}\tan^{-1}\text{x}+\frac{1}{5}\log|\text{x}+2|+\text{C},$ then

A
$\text{a}=-\frac{1}{10},\text{ b}=\frac{2}{5}$
B
$\text{a}=\frac{1}{10},\text{ b}=\frac{2}{5}$
✓
$\text{a}=-\frac{1}{10},\text{ b}=\frac{2}{5}$
D
$\text{a}=\frac{1}{10},\text{ b}=\frac{2}{5}$

Answer: C.

View full solution →

Q 6Answer the following questions in short.1 Mark

Evaluate the following integrals:
$\int\text{x}^4\text{dx}$

View full solution →

Q 7Answer the following questions in short.1 Mark

Evaluate $\int\frac{1-\sin\text{x}}{\cos^2\text{x}}\text{ dx}$

View full solution →

Q 8Answer the following questions in short.1 Mark

Evaluate the following integrals:
$\int\log_\text{x}\text{xdx}$

View full solution →

Q 9Answer the following questions in short.1 Mark

Evaluate $\int\sec^2(7-4\text{x})\text{dx}$

View full solution →

Q 10Answer the following questions in short.1 Mark

Evaluate the following integrals:
$\int3^\text{x}\text{dx}$

View full solution →

Q 11Solve the Following Question.(2 Marks)2 Marks

Evaluate the following integrals:
$\int\frac{1}{\text{x}^5}\text{dx}$

View full solution →

Q 12Solve the Following Question.(2 Marks)2 Marks

Evaluate:
$\int\frac{\text{e}^{6\log_\text{e}\text{x}}-\text{e}^{5\log_\text{e}\text{x}}}{\text{e}^{4\log_\text{e}\text{x}}-\text{e}^{3\log_\text{e}\text{x}}}\text{dx}$

View full solution →

Q 13Solve the Following Question.(2 Marks)2 Marks

Evaluate the following integrals:
$\int(\sec^2\text{x}+\text{cosec}^2\text{x})\text{dx}$

View full solution →

Q 14Solve the Following Question.(2 Marks)2 Marks

Evaluate $\int\frac{\text{x}^3-\text{x}^2+\text{x}+1}{\text{x}-1}\text{ dx}$

View full solution →

Q 15Solve the Following Question.(2 Marks)2 Marks

Evaluate the following integrals:
$\int(3\text{x}+4)^2\text{dx}$

View full solution →

Q 16Solve the Following Question.(3 Marks)3 Marks

Evaluate the following integrals:
$\int(\tan\text{x}+\cot\text{x})^2\text{dx}$