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Warning: The hard deadline has passed. You can attempt it, but you will not get credit for it. You are welcome to try it as a learning exercise.

Quiz 2: There is one question for each of the 10 topics from week 2. The time limit is 1 hour and you only get one try so make sure you have your notes and the week 2 slides handy. Good luck! Hint: you can enter the value

∞ $\infty$ by typing

Inf $Inf$ , and you can use

c $c$ for constant of integration.

In accordance with the Coursera Honor Code, I (Anonymous Student) certify that the answers here are my own work.

Question 1

Use the area interpretation to evaluate the definite integral

∫1−1(1−|x|)dx $\displaystyle \int_{-1}^{1} (1 - |x|) \, dx$ .

Help

Question 2

Use the Fundamental Theorem of Calculus to evaluate the definite integral

∫1−1(1−|x|)dx $\displaystyle \int_{-1}^{1} (1 - |x|) \, dx$ . (please provide answer as a numerical response.)

Help

Question 3

Find

T $T$ such that

∫T012−x54dx=1 $\displaystyle \int_{0}^{T} \frac{12 - x}{54} \, dx = 1$ . (please provide answer as a numerical response.)

Help

Question 4

Use integration by parts to compute the indefinite integral

∫xsin(x)dx $\displaystyle \int x \, \sin(x) \, dx$ .

Help

Question 5

Use integration by substitution to evaluate the definite integral

∫1−1x2cos(x3+3)dx $\displaystyle \int_{-1}^{1} x^{2} \, \cos(x^{3} + 3) \, dx$ . Express your answer using the

sin $\sin$ function.

Help

Question 6

Find values of

a $a$ and

b $b$ such that

x2−6x=(x−a)2+b $x^{2} - 6x = (x - a)^{2} + b$ . Answer this question by entering exactly 2 numeric values separated by a space (the first corresponds to

a $a$ and the second to

b $b$ ). (please provide answers as a numerical response.)

Question 7

Find the derivative of

f(t)=∫t20exdx $\displaystyle f(t) = \int_{0}^{t^{2}} e^{x} \, dx$ .

Help

Question 8

Compute

∫∞11x2dx $\displaystyle \int_{1}^{\infty} \frac{1}{x^{2}} \, dx$ . (please provide answer as a numerical response.)

Help

Question 9

Compute

∫101xdx $\displaystyle \int_{0}^{1} \frac{1}{x} \, dx$ .

Help

Question 10

Compute

ddx[∫x−∞e−t2dt] $\displaystyle \frac{d}{dx} \left[ \int_{-\infty}^{x} e^{-t^{2}} \, dt \right]$ .

Help

In accordance with the Coursera Honor Code, I (Anonymous Student) certify that the answers here are my own work.

You cannot submit your work until you agree to the Honor Code. Thanks!

Mathematical Methods for Quantitative Finance

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Mathematical Methods for Quantitative Finance
by Dr. Kjell Konis

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Mathematical Methods for Quantitative Finance

Mathematical Methods for Quantitative Financeby Dr. Kjell Konis

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Mathematical Methods for Quantitative Finance
by Dr. Kjell Konis