Basic Integration Example in Calculus

# Tag: Mathematics

Differential and Integral Calculus by Feliciano and Uy, Exercise 1.1, Problem 7

Differential and Integral Calculus by Feliciano and Uy, Exercise 1.1 Problem 6

Differential and Integral Calculus by Feliciano and Uy, Exercise 1.1 Problem 5

Differential and Integral Calculus by Feliciano and Uy, Exercise 1.1 Problem 4

Differential and Integral Calculus by Feliciano and Uy, Exercise 1.1 Problem 3

If $latex y=\frac{x^2+3}{x}&s=3&fg=000000$, find x as a function of y. SOLUTION: $latex y=\frac{x^2+3}{x}&s=1&fg=000000$ $latex xy=x^2+3&s=1&fg=000000$ $latex x^2-xy+3=0&s=1&fg=000000$ Solve for x using quadratic formula. We have $latex a=1,\:b=-y,\:and\:c=3&s=1&fg=000000$ $latex x=\frac{-b\pm \sqrt{b^2-4ac}\:}{2a}&s=1&fg=000000$ $latex x=\frac{\cdot -\left(-y\right)\pm \sqrt{\left(-y\right)^2-4\left(1\right)\left(3\right)}}{2\left(1\right)}&s=1&fg=000000$ $latex x=\frac{y\pm \sqrt{y^2-12}}{2}&s=1&fg=000000$

Questions: There is a rack of 15 billiard balls. Balls numbered 1 through 8 are solid-colored. Balls numbered 9 through 15 contain stripes. If one ball is selected at random, determine the odds against it being solid-colored. A certain lottery requires players to select 4 different numbers, in any order, from 1 to 56 inclusive. … Continue reading Northern Essex Community College, Quantitative Reasoning-MAT122-01A, Spring 2017: Exam #2

Soccer fields vary in size. A large soccer field is 115 m long and 85 m wide. What are its dimensions in feet and inches?

American football is played on a 100-yd-long field, excluding the end zones. How long is the field in meters? (Assume that 1 meter equals 3.281 feet.)