Question

Question in comments.

Answer 1

\[\int\limits_{4}^{6}x^3xdx = 260 , \int\limits_{4}^{6} xdx=10, \int\limits_{4}^{6}dx=2\]
evaluate
\[\int\limits_{4}^{6}(x^3+3)dx\]

Answer 2

I have the answer and I'm not really sure how to come to it.

Answer 3

Theres a typo in the first one it should just be x^3dx

Answer 4

Key definite/indefinite integral properties that are useful here :
\[\int\limits_a^b [f(x) + g(x) ]\, dx ~= ~ \int\limits_a^b f(x)\,dx + \int\limits_a^b g(x)\,dx \]
\[\int\limits_a^b cf(x)\,dx = c\int\limits_a^b f(x)\, dx\]

Answer 5

they show the linearity of integration

Answer 6

Alright so seperate it into \[\int\limits_{4}^{6}x^3dx + \int\limits_{4}^{6} 3dx\]

then
\[\int\limits_{4}^{6}x^3dx + 3\int\limits_{4}^{6}dx\]

then I can say 260 + 3(2) = 266

Answer 7

Thanks @ganeshie8 makes a lot of sense now.

Answer 8

Looks perfect! yw :)