alleryStart learning →A student applies the power rule to x^5. What antiderivative results?
- 5x^4 + c
- x^6 + c
- x^6/6 + c
- x^4/4 + c
Show answer and solution
Correct answer: C. x^6/6 + c
The power rule raises the exponent by one and divides by the new exponent, giving x^6/6.
MHT-CET Indefinite Integration — practice questions
Explore 70 free Indefinite Integration questions in MHT-CET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
Practise Indefinite Integration with Quill →Indefinite Integration questions and exercises with answers
Showing questions 1–30 of 70.
A student applies the power rule to x^5. What antiderivative results?Read the answer and worked solution →d/dx of which function gives cos x?Read the answer and worked solution →Integrating sin x gives which result?Read the answer and worked solution →What does integrating sec^2 x produce?Read the answer and worked solution →Which function results on integrating sec x tan x?Read the answer and worked solution →For nonzero x, which function has derivative 1/x?Read the answer and worked solution →If a is a positive constant, what is the primitive of a^x?Read the answer and worked solution →Integrating the function e^(3x) over x yields which expression?Read the answer and worked solution →Which result comes from integrating cos(4x)?Read the answer and worked solution →Find the antiderivative of sin(2x + 3) as a function of x.Read the answer and worked solution →The primitive of the cube (2x + 1)^3 is which expression?Read the answer and worked solution →Which expression integrates sec^2(5x - 4) correctly?Read the answer and worked solution →Integrating the reciprocal 1/(3x - 2) gives which function?Read the answer and worked solution →Term by term, what does the sum x^3 + 3x integrate to?Read the answer and worked solution →The integral of [f(x) + g(x)] dx is equal toRead the answer and worked solution →Why does an indefinite integral carry an arbitrary constant c?Read the answer and worked solution →The integral of 2x gives y = x^2 + c, which representsRead the answer and worked solution →All curves y = x^2 + c have what tangent slope at x = 2?Read the answer and worked solution →Writing tan x as sin x over cos x, what is its integral?Read the answer and worked solution →What is obtained on integrating cosec x with respect to x?Read the answer and worked solution →Substituting t = f(x), what does f'(x)/f(x) integrate to?Read the answer and worked solution →Put t = f(x). Then f'(x) over sqrt(f(x)) integrates to what?Read the answer and worked solution →Find I where I = e^x/(e^x + 1) integrated over x.Read the answer and worked solution →After substituting t = log x, 1/(x log x) integrates to what?Read the answer and worked solution →A student substitutes t = x^2 in x e^(x^2). The integral is?Read the answer and worked solution →Using the identity for sec^2 x, tan^2 x integrates to what?Read the answer and worked solution →Using cosec^2 x - 1, the function cot^2 x integrates to what?Read the answer and worked solution →With the double angle identity, cos^2 x integrates to what?Read the answer and worked solution →Which antiderivative is obtained for sin^2 x?Read the answer and worked solution →Writing 1 as sin^2 x + cos^2 x, what is the antiderivative of 1/(sin^2 x cos^2 x)?Read the answer and worked solution →
Worked practice questions
d/dx of which function gives cos x?
- -cos x + c
- -sin x + c
- sin x + c
- sec x + c
Show answer and solution
Correct answer: C. sin x + c
The derivative of sin x is cos x, so the integral of cos x is sin x plus a constant.
Integrating sin x gives which result?
- -sin x + c
- cos x + c
- -cos x + c
- sin x + c
Show answer and solution
Correct answer: C. -cos x + c
The derivative of cos x is -sin x, so the integral of sin x is -cos x plus a constant.
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