Definite Integrals - Rajasthan Board (RBSE) STD 12 Science MATHS Questions

Q 1M.C.Q (1 Marks)1 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:

$0$
$\frac{\pi}{2}$
$\frac{\pi}{4}$
none of these.

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Q 2M.C.Q (1 Marks)1 Mark

$\int\limits^\frac{\pi}{2}_{-\frac{\pi}{2}}\sin|\text{x}|\text{dx}$ is equal to:

1
2
-1
-2

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Q 3M.C.Q (1 Marks)1 Mark

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

$\frac{\pi^2}{4}$
$\frac{\pi^2}{2}$
$\frac{3\pi^2}{2}$
$\frac{\pi^2}{2}$

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Q 4M.C.Q (1 Marks)1 Mark

The value of $\int\limits^1_0\tan^{-1}\Big(\frac{2\text{x}-1}{1+\text{x}-\text{x}^2}\Big)\text{ dx},$ is:

1
0
-1
$\frac{\pi}{4}$

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Q 5M.C.Q (1 Marks)1 Mark

If $\int\limits^\alpha_0\frac{1}{1+4\text{x}^2}\text{ dx}=\frac{\pi}{8},$ then a equals:

$\frac{\pi}{2}$
$\frac{1}{2}$
$\frac{\pi}{4}$
$1$

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Q 62 Marks Questions2 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 72 Marks Questions2 Marks

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

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Q 82 Marks Questions2 Marks

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

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Q 92 Marks Questions2 Marks

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

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Q 102 Marks Questions2 Marks

Evaluate the following integrals:
$\int\limits^{\frac{\pi}{2}}_0\sqrt{1-\cos2\text{x}}\text{ dx}$

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Q 113 Marks Question3 Marks

Evaluate the following definite integrals:
$\int_{0}^\limits{1}\text{x}(1-\text{x})^5\text{ dx}$

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Q 123 Marks Question3 Marks

Evaluate the following integrals:
$\int_{0}^\limits{1}\frac{\text{e}^\text{x}}{1+\text{e}^{2\text{x}}}\text{ dx}$

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Q 133 Marks Question3 Marks

Evaluate the following integrals:
$\int_{0}^\limits{1}\text{xe}^{\text{x}^2}\text{ dx}$

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Q 143 Marks Question3 Marks

Evaluate the following definite integrals:
$\int_{\frac{\pi}{4}}^\limits{\frac{\pi}{2}}\cot\text{x}\text{ dx}$

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Q 153 Marks Question3 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 165 Marks Questions5 Marks

Evaluate the following integrals:
$\int\limits^{\text{a}}_0\text{x}\sqrt{\frac{\text{a}^2-\text{x}^2}{\text{a}^2+\text{x}^2}}\text{ dx}$

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Q 175 Marks Questions5 Marks

Evaluate the following integrals:
$\int\limits_{0}^{\frac{\pi}{2}}\frac{\text{dx}}{\text{a}\cos\text{x}+\text{b}\sin\text{x}}\text{ a},\text{b}>0$

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Q 185 Marks Questions5 Marks

Evaluate the following integrals:
$\int\limits_{0}^{\frac{\pi}{4}}\Big(\sqrt{\tan\text{x}}+\sqrt{\cot}\text{x}\Big)\text{dx}$

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Q 195 Marks Questions5 Marks

Evaluate the following integrals:
$\int\limits_{0}^{1}\tan^{-1}\text{x dx}$

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Q 205 Marks Questions5 Marks

Evaluate the following definite integrals:
$\int\limits_{0}^{\infty}\frac{1}{\text{a}^2+\text{b}^2\text{x}^2} \text{ dx}$

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Definite Integrals MATHS - Definite Integrals

Definite Integrals question types

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