Antiderivatives Of Trig Functions
For antiderivatives involving both exponential and trigonometric functions see list of integrals of exponential functions. The fundamental theorem of calculus states the relation between differentiation and integration.
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Antiderivative of fractions 1 x 1 x 2 1 x 3 8.
Antiderivatives of trig functions. Cosxdx sinx c in the video we work out the antiderivatives of the four remaining trig functions. Line integral of a scalar field. Gradient of a scalar function.
List of derivatives of trig inverse trig functions. For a complete list of antiderivative functions see lists of integrals. You can represent the entire family of antiderivatives of a function by adding a constant to a known antiderivative.
When the trig functions start with c the differentiation or integration is negative cos and csc. Example 1 y arctan frac 1 x. List of derivatives of log and exponential functions.
For the special antiderivatives involving trigonometric functions see trigonometric integral. If we know f x is the integral of f x then f x is the derivative of f x. List of derivatives of simple functions.
Recall the definitions of the trigonometric functions. In the examples below find the derivative of the given function. Look at the formulas and see how this makes sense.
Generally if the function sin x displaystyle sin x is any trigonometric function and cos x. The following indefinite integrals involve all of these well known trigonometric functions. For the functions other than sin and cos there s always either one tan and two secants or one cot and two cosecants on either side of the formula.
Some of the following trigonometry identities may be needed. Line integral of a vector field. Divergence of a vector field.
The antiderivatives of tangent and cotangent are easy to compute but not so much secant and cosecant. The derivatives of 6 inverse trigonometric functions considered above are consolidated in the following table. A function f x is an antiderivative of f on an interval i if f x f x for all x in i.
Click or tap a problem to see the solution. Here are some hints to help you remember the trig differentiation and integration rules. Listed are some common derivatives and antiderivatives.
The following is a list of integrals antiderivative functions of trigonometric functions. So if f x is the antiderivative of f x then the family of the antiderivatives would be f x c. Depending upon your instructor you may be expected to memorize these antiderivatives.
Antiderivative of e x e 2x and a x exponential functions. Antiderivative of trig functions sin 2x and cos 2x 9. Curl of a vector field.
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