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

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Integration of Exponential Functions
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Integration vs differentiation

Reverse process of differentiation

Primitive (antiderivative)

Working backwards from derivative to find original function

∫ex dx=\int e^x \, dx =

ex+Ce^x + C

∫eax+b dx=\int e^{ax+b} \, dx =

1aeax+b+C\frac{1}{a}e^{ax+b} + C

Coefficient of xx in exponent when integrating eax+be^{ax+b}

Becomes the denominator in the result

CC in integration

Arbitrary constant of integration

Evaluating [F(x)]ab=[F(x)]_a^b =

F(b)−F(a)F(b) - F(a)

Odd function over symmetric interval [−a,a][-a, a] integral

Always zero

∫ef(x)f′(x) dx=\int e^{f(x)} f'(x) \, dx = (reverse chain rule)

ef(x)+Ce^{f(x)} + C

Finding CC in indefinite integral

Use given boundary condition to solve for CC

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