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INTEGRALS Maths - INTEGRALS

Gujarat Board (GSEB) - STD 12 Science - Maths (GSEB - English Medium). 1,218 questions in this chapter.

Question types

INTEGRALS question types

1,218 questions across 6 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

1,218
Questions
6
Question groups
5
Question types
Sample Questions

INTEGRALS questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 3M.C.Q (1 Marks)1 Mark
$\int\frac{2}{(\text{e}^{\text{x}}+\text{e}^{-\text{x}})^2}\text{ dx}=$
  1. $\frac{-\text{e}^{-\text{x}}}{\text{e}^{\text{x}}+\text{e}^{-\text{x}}}+\text{C}$
  2. $-\frac{1}{\text{e}^{\text{x}}+\text{e}^{-\text{x}}}+\text{C}$
  3. $\frac{-1}{(\text{e}^{\text{x}}+1)^2}+\text{C}$
  4. $\frac{1}{\text{e}^{\text{x}}-\text{e}^{-\text{x}}}+\text{C}$
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Q 4M.C.Q (1 Marks)1 Mark
$\int\frac{\text{e}^{\text{x}}(1+\text{x})}{\cos^2(\text{x}\text{e}^{\text{x}})}\text{ dx}=$
  1. $2\log_\text{e}\cos(\text{xe}^{\text{x}})+\text{C}$
  2. $\sec(\text{xe}^{\text{x}})+\text{C}$
  3. $\tan(\text{xe}^{\text{x}})+\text{C}$
  4. $\tan(\text{x}+\text{e}^{\text{x}})+\text{C}$
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Q 5M.C.Q (1 Marks)1 Mark
The symbol dx represents:
  1. The differential of the variable x
  2. The variable of integration is x
  3. Integral with respect to x
  4. None of the above
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Q 6Assertion (A) & Reason (B) MCQ1 Mark
Directions: In these questions, a statement of Assertion is followed by a statement of Reason is given.Choose the correct answer out of the following choices:
Assertion: $\int\sin3\text{x}\cos5\text{x}\text{ dx}=\frac{-\cos8\text{x}}{16}+\frac{\cos2\text{x}}{4}+\text{C}$
Reason: $2\cos\text{A}\sin\text{B}=\sin(\text{A+B})-\sin(\text{A-B})$
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  2. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  3. Assertion is correct statement but Reason is wrong statement.
  4. Assertion is wrong statement but Reason is correct statement.
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Q 7Assertion (A) & Reason (B) MCQ1 Mark
Directions: In these questions, a statement of Assertion is followed by a statement of Reason is given.Choose the correct answer out of the following choices:
Assertion: $\int_{0}^{2\pi}\sin^3\text{x}\text{ dx}=0$
Reason: $\sin^3\text{x}$  an odd function.
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  2. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  3. Assertion is correct statement but Reason is wrong statement.
  4. Assertion is wrong statement but Reason is correct statement.
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Q 8Assertion (A) & Reason (B) MCQ1 Mark
Directions: In these questions, a statement of Assertion is followed by a statement of Reason is given.Choose the correct answer out of the following choices:
Assertion: The value of $\int_{0}^{\frac{\pi}{0}}\sin^6\text{xdx}=\frac{5\pi}{16}$
Reason: If $\text{n}$ is even, then $\int_{0}^{\frac{\pi}{0}}\sin^\text{n}\text{xdx}$ equals.
$\frac{\text{n-1}}{\text{n}}\frac{\text{n}-3}{\text{n}-2}\frac{\text{n-5}}{\text{n-4}}...\frac{1}{2}\frac{\pi}{2}$
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  2. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  3. Assertion is correct statement but Reason is wrong statement.
  4. Assertion is wrong statement but Reason is correct statement.
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Q 9Assertion (A) & Reason (B) MCQ1 Mark
Directions: In these questions, a statement of Assertion is followed by a statement of Reason is given.Choose the correct answer out of the following choices:
Assertion: $\text{I}=\int_{0}^{1}\frac{\text{dx}}{3\sqrt{1+\text{x}^3}}=\int_{0}^{{2}^\frac{-1}{3}}\frac{\text{dt}}{1-\text{t}^3}$
Reason: The integrand of the integral I becomes rational by the substitution $\text{t}=\frac{\text{x}}{3\sqrt{1+\text{x}^3}}$
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  2. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  3. Assertion is correct statement but Reason is wrong statement.
  4. Assertion is wrong statement but Reason is correct statement.
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Q 10Assertion (A) & Reason (B) MCQ1 Mark
Directions: In these questions, a statement of Assertion is followed by a statement of Reason is given.Choose the correct answer out of the following choices:
Assertion: The function F(x) satisfies $\text{F(x}+\pi)=\text{F}\text{(x)}$ for all real $\text{x}$
Reason: $\text{Sin}^2(\text{x}+\pi)=\sin^2\text{x}$ for all real $\text{x}$
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  2. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  3. Assertion is correct statement but Reason is wrong statement.
  4. Assertion is wrong statement but Reason is correct statement.
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Q 151 Marks1 Mark
If $\text{f}(\text{x}) = \int\limits_{0}^{\text{x}}\text{t}\sin\text{t }\text{dt},$then write the value of f'(x).
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Q 284 Marks4 Marks
Evaluate:
$\int\limits^{\pi/4}_{0}\bigg(\frac{\sin \text{x} +\cos \text{x}}{3 + \sin 2\text{x}}\bigg)\text{dx}$
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