Question

Calculus 2 - Indefinite Integrals

Answer 1

\(\large \mathbb{\int_a^b \left( c_1 g(x) + (c_2f(x))^2 \right) dx} \)

\(\large \mathbb{\int_a^b c_1 g(x) dx + \int_a^b (c_2f(x))^2 dx} \)

\(\large \mathbb{c_1\int_a^b g(x) dx + (c_2)^2\int_a^b (f(x))^2 dx} \)

Answer 2

substitute the given values

Answer 3

still stuck on this ?

Answer 4

yes I'm still not sure

Answer 5

You can change the definite integral g(x)dx to g(t)dt if it would help:
\[\large \mathbb{c_1\int\limits_a^b g(x) dx + (c_2)^2\int\limits_a^b (f(x))^2 dx} = \mathbb{c_1\int\limits_a^b g(t) dt + (c_2)^2\int\limits_a^b (f(x))^2 dx} \]

Answer 6

\[\mathbb{\int\limits\limits_a^b g(t) dt = 2 \quad \text{and}\quad \mathbb{\int\limits\limits_a^b (f(x))^2 dx} = 12}\]Just substitute the above two values on the right hand side.

Answer 7

Oh ok, 12+2 = 14?

Answer 8

Don't forget the constants c1 and c2.

Answer 9

\[\Large 2c_1 + 12(c_2)^{2}\]

Answer 10

Thank you

Answer 11

You are welcome.