Mathematics

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


ANSWER

$$\int _{ b }^{ a }{ f\left( x+c \right) } dx$$


SOLUTION

$$Let\>x+c\>=\>t\\dx=dt\\at\>x=a-c,\>t=x+c=a\\at\>x=b-c,\>t=x+c=b\\I=\int\>_{\>a\>}^{\>b\>}f(t)\>dt\\=\int\>_{\>a\>}^{\>b\>}f(x+c)dx$$

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Single Correct Medium Published on 17th 09, 2020
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