If f is integrable on [0, a],then the functio | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) If a function $f$ is integrable on $[0, a]$,then any function derived from it by a linear transformation of the variable,such as $f(a-x)$,is also

Vedclass · Accepted Answer

$f(a-x)$

Vedclass · Answer

(A) If a function $f$ is integrable on $[0, a]$,then any function derived from it by a linear transformation of the variable,such as $f(a-x)$,is also integrable on $[0, a]$.This is a standard property of Riemann integrable functions.Specifically,if $f$ is integrable on $[0, a]$,then the composition $f(a-x)$ is integrable on $[0, a]$ because the transformation $u = a-x$ is a continuous and monotonic mapping.Therefore,$f(a-x)$ is integrable on $[0, a]$.Thus,option $A$ is correct.

If $f$ is integrable on $[0, a]$,then the function $h$ defined on $[0, a]$ as $h(x) = \int_0^x f(t) dt$ is integrable on $[0, a]$. Which of the following functions is also integrable on $[0, a]$?

Similar Questions

$\int_{1}^{3} (x - 1)(x - 2)(x - 3) \, dx = $

Suppose that $f$ and $g$ are integrable on $[a, b]$,then $f+g$ is integrable on ......... .

$\int_0^1 x \tan^{-1} x \, dx = $

The total number of distinct $x \in [0, 1]$ for which $\int_0^x \frac{t^2}{1+t^4} dt = 2x - 1$ is

The value of $\alpha$ for which $4 \alpha \int_{-1}^{2} e^{-\alpha |x|} dx = 5$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module