Home › TS EAPCET (Engineering) › Mathematics › Integration by Substitution › What is the integral of the product x(1 − x) tak…
What is the integral of the product x(1 − x) taken over the unit interval?
A1/12
B1/2
C1/3
D1/6
Answer & Solution
Correct answer: D. 1/6
Expanding gives x − x², whose integral from 0 to 1 is 1/2 − 1/3 = 1/6.
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?