Integral Calculus | MATHalino reviewer about Integral Calculus

Problem
Evaluate $\displaystyle \int_0^1 \dfrac{x \, dx}{x^2 + 2}$.

A. 0.2027	C. 0.2270
B. 0.2207	D. 0.2072

Problem
Find the equation of the curve passing through the point (3, 2) and having s slope 5x² - x + 1 at every point (x, y).

A. $y = \frac{5}{3}x^3 - \frac{1}{2}x^2 + x - \frac{31}{3}$	C. $y = 5x^3 - 2x^2 + x - 118$
B. $y = 5x^3 - 2x^2 + x - 31$	D. $y = \frac{5}{3}x^3 - \frac{1}{2}x^2 + x - \frac{83}{2}$

Problem
Given the position function x(t) = t⁴ - 8t², find the distance that the particle travels at t = 0 to t = 4.

A. 160	C. 140
B. 150	D. 130

Problem
Evaluate $\displaystyle \int_0^9 \dfrac{1}{\sqrt{1 + \sqrt{x}}}$

A. 4.667	C. 5.333
B. 3.227	D. 6.333