Flashcards in 9.1.3 Antiderivatives of Trigonometric and Exponential Functions Deck (11):
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.
- 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
- To evaluate this indefinite integral, start by applying
the sum rule.
- Now you can evaluate the integral of each term
- 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.
Find f(x) so that f′(x)=−4e^x−6sinx.
−4e^ x + 6 cos x + C
Evaluate the integral. ∫sec^2xdx
tanx + C
Evaluate the integral. ∫sinx dx
− cos x + C
Evaluate the integral: ∫(2sinx+3cosx) dx.
−2 cos x + 3 sin x + C
Evaluate the integral ∫sin2x/cosx dx.
−2 cos x + C
Evaluate: ∫secx(tanx+secx) dx.
sec x + tan x + C
Evaluate the integral: ∫(1+sin^2θcscθ) dθ
Evaluate the integral:∫3exdx.