Question

Integrate:

${\int }_{a-c}^{b-c}f(x+c)dx$ equals ?

• A. ${\int }_b^{a}f(x+c)dx$
• B. ${\int }_b^{a}f\left(x\right)dx$
• C. ${\int }_{b-2c}^{a-2c}f\left(x\right)dx$
• D. ${\int }_b^{a}f(x+2c)dx$

Answer 1

Answer: (A)

${\int }_b^{a}f(x+c)dx$

$Letx+c=tdx=dtatx=a-c,t=x+c=aatx=b-c,t=x+c=bI=\int {}_a^{b}f\left(t\right)dt=\int {}_a^{b}f(x+c)dx$