Evaluate the integral of (x dx) / (x^2 + 2) with lower limit of 0 and upper limit of 1
Problem
Evaluate $\displaystyle \int_0^1 \dfrac{x \, dx}{x^2 + 2}$.
| A. 0.2027 | C. 0.2270 |
| B. 0.2207 | D. 0.2072 |
Integral Calculus
Find the equation of the curve passing through the point (3, 2) and having s slope 5x^2 - x + 1 at every point (x, y)
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. $y = \frac{5}{3}x^3 - \frac{1}{2}x^2 + x - \frac{83}{2}$ |
The Distance the Particle Travels with Given Position Function x(t) = t^4 - 8t^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 |
Find the Integral of dx / sqrt(1 + sqrt(x))
Problem
Evaluate $\displaystyle \int_0^9 \dfrac{1}{\sqrt{1 + \sqrt{x}}}$
| A. 4.667 | C. 5.333 |
| B. 3.227 | D. 6.333 |
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