9.1.3 Antiderivatives of Trigonometric and Exponential Functions Flashcards Preview

AP Calculus AB > 9.1.3 Antiderivatives of Trigonometric and Exponential Functions > Flashcards

Flashcards in 9.1.3 Antiderivatives of Trigonometric and Exponential Functions Deck (11):
1

Antiderivatives of Trigonometric and Exponential Functions

- Given two functions, f and F, F is an antiderivative of f if F ′ (x ) = f(x ). Antidifferentiation is a process or operation that reverses differentiation.
- Discover integration formulas by looking at differentiation formulas backwards.

2

note

- Here are some antiderivative formulas.
- Notice that some functions that are easy to
differentiate are not as easy to integrate. It is
generally the case that it is easier to differentiate
than integrate.
- To evaluate this indefinite integral, start by applying
the sum rule.
- Now you can evaluate the integral of each term
individually.
- Remember, when using the power rule for
integration, you must multiply by the reciprocal of
the new exponent.
- You can always check that your answer is correct
by taking the derivative.

3

Find f(x) so that f′(x)=−4e^x−6sinx.

−4e^ x + 6 cos x + C

4

Evaluate the integral. ∫sec^2xdx

tanx + C

5

Evaluate the integral. ∫sinx dx

− cos x + C

6

Evaluate the integral: ∫(2sinx+3cosx) dx.

−2 cos x + 3 sin x + C

7

Evaluate the integral ∫sin2x/cosx dx.

−2 cos x + C

8

Evaluate: ∫secx(tanx+secx) dx.

sec x + tan x + C

9

Evaluate the integral: ∫(1+sin^2θcscθ) dθ

θ−cosθ+C

10

Evaluate the integral:∫3exdx.

3e^x+C

11

Evaluate:
∫tan^2xdx

tan x − x + C

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