Question

help, integrals.

Answer 1

given \[\int\limits_{0}^{3}f(x)dx = 4 \int\limits_{3}^{6} f(x)dx = -1 \]

Answer 2

find \[\int\limits_{0}^{6}f(x)dx\]

Answer 3

\[\int\limits_{3}^{6}f(x)dx \int\limits_{3}^{3}f(x) dx \]

Answer 4

From (1): \(\displaystyle\Large\left[\int f(x)dx\right]^3_0=-1\)
From (2): \(\displaystyle\Large\left[\int f(x)dx\right]^6_3=-0.25\)

Answer 5

? no , those are equal to 4 and -1. the 1 above it, and the 2 below it are my questions.

Answer 6

\[\mbox{THEOREM:}\large\int_a^cf(x)dx=\int_a^bf(x)dx+\int_b^cf(x)dx\]

Answer 7

thank you for the theorem.

Answer 8

no problem :)