Integration of Exponential Functions (HSC SSCE Mathematics Advanced): Quizzes

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Integration of Exponential Functions
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What is the relationship between integration and differentiation?

They are inverse operations

What is ∫ex dx\int e^x \, dx equal to?

ex+Ce^x + C

When integrating eax+be^{ax+b}, what must you do with the coefficient aa?

Divide by aa in the result

What is ∫e3x+2 dx\int e^{3x+2} \, dx?

13e3x+2+C\frac{1}{3}e^{3x+2} + C

Evaluate ∫02ex dx\int_0^2 e^x \, dx.

e2−1e^2 - 1

For ∫e5−2x dx\int e^{5-2x} \, dx, what is the value of aa in the standard form?

a=−2a = -2

If f′(x)=exf'(x) = e^x and f(1)=0f(1) = 0, what is the value of constant CC in f(x)=ex+Cf(x) = e^x + C?

C=−eC = -e

What is ∫(1−x+ex) dx\int (1 - x + e^x) \, dx?

x−12x2+ex+Cx - \frac{1}{2}x^2 + e^x + C

What is the result when an odd function is integrated over a symmetric interval [−a,a][-a, a]?

Always zero

What must the integrand contain for the reverse chain rule to be applicable?

A function and its derivative

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