Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integration2 Marks
MCQ
$\int_0^a f(x) d x=$
A
$\int_0^a f(a+x) d x$
B
$\int_0^{ a } f (2 a +x) dx$
C
$\int_0^a f(x-a) d x$
✓
$\int_0^{ a } f ( a -x) dx$
✓
Answer
Correct option: D.
$\int_0^{ a } f ( a -x) dx$
(D) Put $x= a - t \Rightarrow d x=- dt$ When $x=0, t = a$ and when $x= a , t =0$ $\therefore \quad \int_0^{ a } f (x) d x=-\int_{ a }^0 f ( a - t ) dt$ $=\int_0^{ a } f ( a - t ) dt \quad \ldots \left[\because \int_{ a }^{ b } f (x) d x=-\int_{ b }^{ a } f (x) d x\right]$ $=\int_0^{ a } f ( a -x) d x \quad \ldots \left[\because \int_{ a }^{ b } f (x) d x=\int_{ a }^{ b } f ( t ) dt \right]$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.