math quizes calc 1

Math 151 Quiz 13. Name: Due no later than Noon on Wednesday, December 7

I. Find the most general antiderivative of each function. You do not need to show any work. [1] 𝑥!! + 𝑒! + 𝑙𝑛2 General Antiderivative :

2 3 2 𝑥4 3

General Antiderivative :

3 𝑠𝑒𝑐!x + 1

1 + x!

General Antiderivative : [4] cos t + sin t

General Antiderivative :

[5] x!(𝑥! + 1)

General Antiderivative :

3 pt.s each

II. Solve the differential equation with the given conditions. Show every step in great detail. Use proper integral notation.

fʹʹ(x) = 40x3 - 8 f(0) = -7, f(1) = - 6

10 pt.s

J Bonus (1 point) Because this solution contains no arbitrary constants, we call this a solution.

Solution: