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How do you find the integral of 1 COSX?

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How do you find the integral of 1 COSX?

∫ (1 / cos(x)) dx = ∫ sec(x) dx = ln |sec(x) + tan(x)| + C, where C is a constant. The antiderivative of 1 / cos(x) is ln |sec(x) + tan(x)| + C, where C is a constant.

How do you integrate COSX?

What is the Integral of Cos x? The integral of cos x is sin x + C. i.e., ∫ cos x dx = sin x + C. Here, C is the integration constant.

What does Cos integrate to?

By the fundamental theorem of calculus and the fact that the derivative of sin(x) is cos(x), we have that the integral of cos(x) is sin(x) + C, where C is a constant.

How do you turn sin into cos?

All triangles have 3 angles that add to 180 degrees. Therefore, if one angle is 90 degrees we can figure out Sin Theta = Cos (90 – Theta) and Cos Theta = Sin (90 – Theta).

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What is the integration of COSX?

What is the Integral of cos x? The integral of cos x dx is sin x. Mathematically, this is written as ∫ cos x dx = sin x + C, where, C is the integration constant.

What is the integral of sin x?

The integral of sin(x) is found by using the integration techniques known as integration by parts or substitution. Integration by substitution is also known as using the chain rule for derivatives in the reverse.

How to find the antiderivative?

xndx = xn+1+c as long as n does not equal -1. This is essentially the power rule for derivatives in reverse

  • cf (x)dx = c f (x)dx . That is,a scalar can be pulled out of the integral.
  • (f (x)+g(x))dx = f (x)dx+g(x)dx .
  • sin (x)dx = – cos (x)+c cos (x)dx = sin (x)+c sec2(x)dx = tan (x)+c These are the opposite of the trigonometric derivatives.

    • What is the antiderivative of cosx?

    Antiderivative means Integration so it can be shown by another example to understand the antiderivative of cosx as the function is ∫[cos^2 (x)dx] then Since cos (2x)= 2 cos^2(x) – 1, cos^2 (x)= [1 + cos (2x)] /2, ∫ [[ 1 + cos (2x)] /2 dx], or [[1/2]* ∫[1*dx + cos (2x)dx], or [1/2]* ∫ [1*dx ]…

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    What is the integral of Cos?

    The integral of cos(2x) is 1/2 x sin(2x) + C, where C is equal to a constant. The integral of the function cos(2x) can be determined by using the integration technique known as substitution. In calculus, substitution is derived from the chain rule for differentiation.