$\displaystyle \int_1^{7} f(x) dx = 19$ and $\displaystyle \int_5^{7} f(x)dx = 12$
then find
$\displaystyle \int_1^{5} 3f(x) dx $
$\displaystyle \int_1^{7} f(J) dJ $
how would i work this out? cheers
Any constant can be moved inside and outside of an integral freely. So:
$\displaystyle \int_1^{5} 3f(x) dx = 3 \int_{1}^{5}f(x)dx$
Now if we simply use the definition of integral bounds, we can construct these bounds by combining others.
$\displaystyle \int_{1}^{5}f(x)dx=\int_{1}^{7}f(x)dx-\int_{5}^{7}f(x)dx=19-12=7$
Multiply by 3 and I get an answer of 21.