Integrate secx(tanx - secx) dx

Thread starter BuBbLeS01
Start date Nov 16, 2007
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Dx Integrate

In summary, the equation for "Integrate secx(tanx - secx) dx" is ∫secx(tanx - secx) dx. The "∫" symbol represents integration, which is the inverse of differentiation and is used to find the area under a curve or the anti-derivative of a function. To solve this integral, one must use trigonometric identities and the power rule of integration. The domain of this function is all real numbers except for x = nπ/2, and the difference between definite and indefinite integration is that definite integration results in a single numerical value while indefinite integration results in a function with a constant of integration.

Nov 16, 2007

BuBbLeS01

Homework Statement

Integrate...
secx(tanx - secx) dx

The Attempt at a Solution

secxtanx - sec^2x dx =

secx - tanx + C

is that right?

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Nov 16, 2007

rock.freak667

Homework Helper

it is correct

What is the equation for "Integrate secx(tanx - secx) dx"?

The equation is ∫secx(tanx - secx) dx.

What does the "∫" symbol mean in the equation?

The "∫" symbol represents integration, which is a mathematical operation that is the inverse of differentiation. It is used to find the area under a curve or the anti-derivative of a function.

What are the steps to solve "Integrate secx(tanx - secx) dx"?

The steps to solve this integral are:1. Use the trigonometric identity tanx = sinx/cosx to rewrite the integral as ∫secx(sinx/cosx - secx) dx.2. Use the identity secx = 1/cosx to rewrite the integral as ∫sinx - 1 dx.3. Use the power rule of integration to integrate sinx and -1, resulting in -cosx - x + C.4. Simplify the result to obtain the final solution of -cosx - x + C.

What is the domain of the function "Integrate secx(tanx - secx) dx"?

The domain of this function is all real numbers except for x = nπ/2, where n is an integer, as this would result in division by zero.

What is the difference between definite and indefinite integration?

Definite integration involves finding the exact numerical value of an integral within a specified interval, while indefinite integration involves finding the general anti-derivative of a function without specifying limits. In other words, definite integration results in a single numerical value, while indefinite integration results in a function with a constant of integration.