7–64. Integration review Evaluate the following integrals.
12. ∫ from -5 to 0 of dx / √(4 - x)

Let C be the curve parameterized by $x=t^2$, $y=t^3$ for $0\le t\le 1$. Find the value of the line integral ${\int }_C^{}ydx$.

Find the exact length of the curve $y=\frac{1}{4}{x}^2-\frac{1}{2}\ln \left(x\right)$ for $1\le x\le 2$.

Given the parametric equations $x={\sin }^2\left(t\right)$, $y=4\cos \left(t\right)$ for $0\le t\le \pi$, what is the area enclosed by the curve and the y-axis?

Evaluate the double integral of $f(x,y)=x+y$ over the region $R$ bounded by $x=0$, $x=1$, $y=0$, and $y=2$.

7–64. Integration review Evaluate the following integrals.

24. ∫ from 0 to θ of (x⁵⸍² - x¹⸍²) / x³⸍² dx

7–84. Evaluate the following integrals.

19. ∫ from 0 to π/2 [sin⁷x] dx

7–64. Integration review Evaluate the following integrals.

60. ∫ from 0 to π/4 of 3√(1 + sin 2x) dx

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.

(a) If ƒ is symmetric about the line 𝓍 = 2 , then ∫₀⁴ ƒ(𝓍) d𝓍 = 2 ∫₀² ƒ(𝓍) d𝓍.