Science:Math Exam Resources/Courses/MATH103/April 2017/Question 02 (b) (i)

MATH103 April 2017

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Question 02 (b) (i)
Consider the functions $A_{i}(x)$ and calculate their derivatives $A'_{i}(x)={\frac {dA_{i}(x)}{dx}}$ . (i) $A_{1}(x)=\int _{0}^{x}e^{-y^{2}}dy$

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint
Use the fundamental theorem of calculus.

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Solution

Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. Recall the fundamental theorem of calculus: for a continuous function $f$ on the whole real line, the derivative of a function $F$ defined by $F(x)=\int _{0}^{x}f(y)dy$ is $F'(x)=f(x)$. Using this, the derivative of $A_{1}$ is $A_{1}'(x)={\frac {d}{dx}}\int _{0}^{x}e^{-y^{2}}dy=e^{-x^{2}}.$ Answer: $\color {blue}e^{-x^{2}}$