Definite Integrals - Maharashtra Board STD 12 Maths Questions

Q 1MCQ1 Mark

The value of $\int\limits^{\pi}_0\frac{\text{x}\tan\text{x}}{\sec\text{x}+\cos\text{x}}\text{ dx}$ is:

✓
$\frac{\pi^2}{4}$
B
$\frac{\pi^2}{2}$
C
$\frac{3\pi^2}{2}$
D
$\frac{\pi^2}{2}$

Answer: A.

Q 2MCQ1 Mark

$\int\limits^1_0\frac{\text{d}}{\text{dx}}\Big\{\sin^{-1}\Big(\frac{2\text{x}}{1+\text{x}^2}\Big)\Big\}\text{dx}$ is equal to:

A
$0$
B
${\pi}$
✓
$\frac{\pi}{2}$
D
$\frac{\pi}{4}$

Answer: C.

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Q 3MCQ1 Mark

$\int\limits^\sqrt{3}_1\frac{1}{1+\text{x}^2}\text{ dx}$ is equal to:

✓
$\frac{\pi}{12}$
B
$\frac{\pi}{6}$
C
$\frac{\pi}{4}$
D
$\frac{\pi}{3}$

Answer: A.

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Q 4MCQ1 Mark

$\int\limits^{\frac{\pi}{2}}_0\sin2\text{x }\log\tan\text{x dx}$ is equal to:

A
$\pi$
B
$\frac{\pi}{2}$
✓
$0$
D
$2\pi$

Answer: C.

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Q 5MCQ1 Mark

The value of the integral $\int\limits^{\frac{\pi}{2}}_0\frac{\sqrt{\cos\text{x}}}{\sqrt{\cos\text{x}}+\sqrt{\sin\text{x}}}\text{ dx}$ is:

A
$0$
B
$\frac{\pi}{2}$
✓
$\frac{\pi}{4}$
D
none of these.

Answer: C.

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Q 6Solve the Following Question.(2 Marks)2 Marks

Evaluate the following integrals:$\int\limits^\frac{\pi}{2}_{-\frac{\pi}{2}}\text{x}\cos^2\text{x}\text{ dx}$

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Q 7Solve the Following Question.(2 Marks)2 Marks

Evaluate:$\int\limits^3_23^\text{x}\text{ dx}$

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Q 8Solve the Following Question.(2 Marks)2 Marks

Evaluate the following integrals:$\int\limits^{2}_1\log_\text{e}[\text{x}]\text{dx}$

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Q 9Solve the Following Question.(2 Marks)2 Marks

If $\int\limits^1_0(3\text{x}^2+2\text{x}+\text{k})\text{dx}=0,$ find the value of k.

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Q 10Solve the Following Question.(2 Marks)2 Marks

Evaluate the following integrals:$\int\limits^\frac{\pi}{4}_0\tan\text{x dx}$

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Q 11Solve the Following Question.(3 Marks)3 Marks

Evaluate the following integrals:$\int^\limits4_{-4}|\text{x}+2|\text{dx}$

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Q 12Solve the Following Question.(3 Marks)3 Marks

Evaluate the following definite integrals:$\int_{4}^\limits{9}\frac{1}{\sqrt{\text{x}}}\text{ dx}$

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Q 13Solve the Following Question.(3 Marks)3 Marks

Evaluate the following integrals:$\int^\limits1_{-1}5\text{x}^4\sqrt{\text{x}^5+1}\text{ dx}$

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Q 14Solve the Following Question.(3 Marks)3 Marks

Evaluate the following integrals:$\int_{0}^\limits{\frac{1}{2}}\frac{\text{x}\sin^{-1}\text{x}}{\sqrt{1-\text{x}^2}}\text{ dx}$

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Q 15Solve the Following Question.(3 Marks)3 Marks

Evaluate the following integrals:$\int^\limits{\pi}_{0}5\big(5-4\cos\theta\big)^{\frac{1}{4}}\sin\theta\text{ d}\theta$

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Q 16Solve the Following Question.(5 Marks)5 Marks

Evaluate the following integrals:$\int_{\frac{\pi}{6}}^\limits{\frac{\pi}{3}}(\tan\text{x}+\cot\text{x})^2\text{dx}$

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Q 17Solve the Following Question.(5 Marks)5 Marks

Evaluate the following integrals:$\int^\limits{1}_0\big(\cos^{-1}\text{x}\big)^2\text{dx}$

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Q 18Solve the Following Question.(5 Marks)5 Marks

Evaluate the following integrals as limit of sum:$\int\limits^\text{b}_{\text{a}}\cos\text{x dx}$

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Q 19Solve the Following Question.(5 Marks)5 Marks

Evaluate the following integrals:$\int\limits^{\frac{\pi}{3}}_{\frac{\pi}{6}}\frac{1}{1+\sqrt{\tan\text{x}}}\text{ dx}$

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Q 20Solve the Following Question.(5 Marks)5 Marks

Evaluate the following integrals as limit of sum:$\int\limits^2_{1}\text{x}^2\text{ dx}$

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Definite Integrals Maths - Definite Integrals

Definite Integrals question types

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