DSE 2007 Question 42: Integration and its applications

If $f:\Re_{+}\to\Re$ is defined by $f(x)=\int_{x}^{x^{2}}e^{t}\,dt$ , then the derivative of $f$ at $x>0$ is

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If f:ℜ₊→ℜ is defined by f(x)=∫ₓ^(x²)e^t dt, then the derivative of f at x>0 is (A) 2xe^(x²)-e^x (B) 2xe^(x²)+e^x (C) (2x-1)e^(x²) (D) (2x-1)e^x

Also written as: If f: Re_+-> Re is defined by f(x)= integral_x^(x^2)e^t dt, then the derivative of f at x>0 is

Integration and its applications has come up 43 times in 6 exams since 2007.

This question is on Integration techniques, part of Integration and its applications in Mathematics.

Substitution, integration by parts, partial fractions and improper integrals.

TestStop has 12 past-paper questions on this subtopic; the nearest in year are below.

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Plain-text version

If f:ℜ₊→ℜ is defined by f(x)=∫ₓ^(x²)e^t dt, then the derivative of f at x>0 is (A) 2xe^(x²)-e^x (B) 2xe^(x²)+e^x (C) (2x-1)e^(x²) (D) (2x-1)e^x

Also written as: If f: Re_+-> Re is defined by f(x)= integral_x^(x^2)e^t dt, then the derivative of f at x>0 is

Integration and its applications has come up 43 times in 6 exams since 2007.

Question from the DSE 2007 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.