Answer:
324
Step-by-step explanation:
Given:
[tex]g(x)=4x^2+2x\\ \\f(x)=\int\limits^x_0 {g(t)} \, dt[/tex]
Find:
[tex]f(6)[/tex]
First, find f(x):
[tex]f(x)\\ \\=\int\limits^x_0 {g(t)} \, dt\\ \\=\int\limits^x_0 {(4t^2+2t)} \, dt\\ \\=\left(4\cdot \dfrac{t^3}{3}+2\cdot \dfrac{t^2}{2}\right)\big|\limits^x_0\\ \\=\left(\dfrac{4t^3}{3}+t^2\right)\big|\limits^x_0\\ \\= \left(\dfrac{4x^3}{3}+x^2\right)-\left(\dfrac{4\cdot 0^3}{3}+0^2\right)\\ \\=\dfrac{4x^3}{3}+x^2[/tex]
Now,
[tex]f(6)\\ \\=\dfrac{4\cdot 6^3}{3}+6^2\\ \\=288+36\\ \\=324[/tex]
