alleryStart learning →∫ sec² x dx equals:
- csc x + C
- sec x + C
- cot x + C
- tan x + C
Show answer and solution
Correct answer: D. tan x + C
d/dx (tan x) = sec² x, so ∫ sec² x dx = tan x + C.
Indian Navy 10+2 B.Tech Cadet Integrals — practice questions
Explore 25 free Integrals questions in Indian Navy 10+2 B.Tech Cadet Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
Practise Integrals with Quill →Integrals questions and exercises with answers
Showing questions 1–25 of 25.
∫ sec² x dx equals:Read the answer and worked solution →Definite integral ∫₀¹ x² dx equals:Read the answer and worked solution →∫₀^(π/2) sin x dx equals:Read the answer and worked solution →∫₀¹ x e^(x²) dx equals:Read the answer and worked solution →∫₀^(π) sin² x dx equals:Read 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
Definite integral ∫₀¹ x² dx equals:
- 1/3
- 1
- 1/2
- 2/3
Show answer and solution
Correct answer: A. 1/3
We have ∫₀¹ x² dx = [x³/3]₀¹.
That is ∫₀¹ x² dx = 1/3 - 0.
So ∫₀¹ x² dx = 1/3.
∫₀^(π/2) sin x dx equals:
- π/2
- 1
- 0
- 2
Show answer and solution
Correct answer: B. 1
∫ sin x dx = -cos x.
Evaluated from 0 to π/2: -cos(π/2) - (-cos 0) = 0 - (-1) = 1.
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