Question

i really need help with this question,please

Answer 1

\[\int_0^6f(x)dx=\int_0^3f(x)dx+\int_3^6f(x)dx=4-1=3\] for the first one

Answer 2

\[\int_6^3f(x)dx=-\int_3^6f(x)dx=-(-1)=1\] for the second

Answer 3

\[\int_a^af(x)dx=0\] always

Answer 4

@satellite73 thanks !! finally !:D
can i get help with this last one please

Answer 5

\[\int_0^{\pi}x+\sin(x)dx\]

Answer 6

anti derivative is
\[F(x)=\frac{x^2}{2}-\cos(x)\]

Answer 7

find
\[F(\pi)-F(0)\]

Answer 8

i mean that ^^

Answer 9

no

Answer 10

\(\cos(\pi)=-1\)

Answer 11

so it is
\[\frac{\pi ^2}{2}-(-1)+1=2+\frac{\pi ^2}{2}\]

Answer 12

\[F(\pi)-F(0)=\left(\frac{\pi^2}{2}-\cos(\pi)\right)-\left(\frac{0^2}{2}-\cos(0)\right)\]
\[=\frac{\pi^2}{2}-(-1)-(-1)\]