alleryStart learning →By substitution u = x², ∫ 2x sin(x²) dx equals:
- -cos(x²) + C
- -sin(x²) + C
- cos(x²) + C
- sin(x²) + C
Show answer and solution
Correct answer: A. -cos(x²) + C
Let u = x², du = 2x dx.
Integral becomes ∫ sin u du = -cos u + C = -cos(x²) + C.
Indian Navy Pilot Integrals — practice questions
Explore 27 free Integrals questions in Indian Navy Pilot Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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Showing questions 1–27 of 27.
By substitution u = x², ∫ 2x sin(x²) dx equals:Read the answer and worked solution →By partial fractions, ∫ dx/(x(x+1)) equals:Read the answer and worked solution →∫₀^(π/2) sin x cos x dx equals:Read the answer and worked solution →$\displaystyle\int e^x\,dx$ equals:Read the answer and worked solution →The arbitrary constant $C$ added in an indefinite integral is called the:Read the answer and worked solution →$\displaystyle\int 2x\,dx$ equals:Read the answer and worked solution →Order the steps to integrate ∫ x·eˣ dx by partsRead the answer and worked solution →Complete the relationship between the two calculiRead the answer and worked solution →True or false: the constant of integrationRead the answer and worked solution →Differentiation or integration?Read the answer and worked solution →Tap every property of indefinite integrals the chapter givesRead the answer and worked solution →Properties in useRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Order the steps: check an indefinite integralRead the answer and worked solution →Flip and pair: term with meaningRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →True or false: reading the notationRead the answer and worked solution →Definite or indefinite?Read the answer and worked solution →Reading the definitions backRead the answer and worked solution →Complete the linearity rulesRead the answer and worked solution →Which process is being described?Read the answer and worked solution →True or false: what the constant meansRead the answer and worked solution →Checking an integralRead the answer and worked solution →Tap every true statement about integrationRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →
Worked practice questions
By partial fractions, ∫ dx/(x(x+1)) equals:
- ln |x| + C
- ln |x(x+1)| + C
- ln |x/(x+1)| + C
- arctan x + C
Show answer and solution
Correct answer: C. ln |x/(x+1)| + C
1/(x(x+1)) = 1/x - 1/(x+1).
We have ∫ = ln |x| - ln |x+1| + C.
So ∫ = ln |x/(x+1)| + C.
∫₀^(π/2) sin x cos x dx equals:
- π/4
- 1/2
- 0
- 1
Show answer and solution
Correct answer: B. 1/2
sin x cos x = (1/2) sin(2x).
**So integral = (1/2) ∫₀^(π/2) sin(2x) dx = (1/2)[-cos(2x)/2]₀^(π/2) = (1/4)[1 - (-1)] = 1/2.**
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