Home › MHT-CET › Mathematics › Definite Integration › Using the King's property, $\int_0^a f(x)\,dx$ e…
Using the King's property, $\int_0^a f(x)\,dx$ equals:
A$\int_0^a f(a-x)\,dx$
B$\int_0^a f(a+x)\,dx$
C$\int_0^a f(x-a)\,dx$
D$-\int_0^a f(x)\,dx$
Answer & Solution
Correct answer: A. $\int_0^a f(a-x)\,dx$
Special case of King's property with $b = a$, lower = 0: $\int_0^a f(x)\,dx = \int_0^a f(0+a-x)\,dx = \int_0^a f(a-x)\,dx$.
Related questions
Using definite integration as the limit of a sum, $\int_1^2 (2x + 5)\,dx$ equals:$\int_0^{\pi/2} \cos^2 x\,dx$ equals:$\int_0^{\pi/2} qrt{1 - \cos 4x}\,dx$ equals:Using the King's property, evaluate $\int_0^{\pi/2} \dfrac{dx}{1 + qrt[3]{\tan x}}$:$\int_1^2 \dfrac{\log x}{x^2}\,dx$ equals:$\int_{-1}^{1} |5x - 3|\,dx$ equals:Evaluate $\int_2^3 7^x\,dx$:$\int_0^4 (x - x^2)\,dx$ equals: