Answer to Question #180671 in Calculus for Joe

Question

1b Integrate the following expressions.

∫(3𝑥3−4𝑥2+5𝑥−3)𝑑𝑥

∫(3𝑐𝑜𝑠2𝜃+5𝑐𝑜𝑠4𝜃)𝑑𝜃

Answer 1

1) $∫(3𝑥^3−4𝑥^2+5𝑥−3)𝑑𝑥=3\int x^3dx-4\int x^2dx+5 \int xdx-3\int 1 \ dx$

$\Rightarrow \dfrac{3}{4}x^4-\dfrac{4}{3}x^3 +\dfrac{5}{2}x^2-3x+C$

2) $\int(3cos2\theta+5cos4\theta)d\theta=3\int cos2\theta d\theta+5\int cos4\theta d\theta$

$\Rightarrow \dfrac{3}{2}sin2\theta+\dfrac{5}{4}sin4\theta+C$