Home › TS EAPCET (Engineering) › Mathematics › Integration by Substitution › Differentiating the accumulated integral of t² f…
Differentiating the accumulated integral of t² from 0 to x gives which function?
A2x
B3x²
Cx²
Dx³/3
Answer & Solution
Correct answer: C. x²
The first part of the theorem states that differentiating an integral with variable upper limit returns the integrand at x, which is x².
Related questions
How can the result of an integration by substitution be checked?Using u = x² + 1, the integral of x(x² + 1)³ between x = 0 and x = 2 evaluates toIn ∫₀² x(x² + 1)³ dx, the substitution u = x² + 1 changes the limits toIf F is an antiderivative of a continuous f, then the integral of f from a to b equalsThe fundamental theorem of calculus shows that differentiation and integration areIn the LIATE rule for choosing u, which type of function comes first in the list?By the LIATE rule, which factor should be chosen as u when integrating x cos x?Integration by substitution is the integral counterpart of which differentiation rule?