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 AA (Artificer Apprentice) Integrals — practice questions
Explore 23 free Integrals questions in Indian Navy AA (Artificer Apprentice) 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 1–23 of 23.
∫ sec² x dx equals:Read the answer and worked solution →The technique used to integrate a product of two functions is called:Read the answer and worked solution →Compute ∫ 2x sin(x²) dx using substitution: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
The technique used to integrate a product of two functions is called:
- integration by parts
- substitution only
- partial fractions
- differentiation
Show answer and solution
Correct answer: A. integration by parts
Products of two functions are integrated using integration by parts (∫u dv = uv − ∫v du).
Compute ∫ 2x sin(x²) dx using substitution:
- $\sin(x^2) + C$
- $\cos(x^2) + C$
- $-\cos(x^2) + C$
- $x^2 \cos(x^2) + C$
Show answer and solution
Correct answer: C. $-\cos(x^2) + C$
Let u = x², du = 2x dx
→ ∫sin(u) du = -cos(u) + C = -cos(x²) + C. Substitution exploits the chain rule in reverse.
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