Evaluate the given integrals.

a. {eq}\int_{-1}^{1} |2x-1|dz{/eq}

b. {eq}\int_{0}^{\frac{3 \pi}{4}} |\cos x|dx{/eq}


Evaluate the given integrals.

a. {eq}\int_{-1}^{1} |2x-1|dz{/eq}

b. {eq}\int_{0}^{\frac{3 \pi}{4}} |\cos x|dx{/eq}

Definite Integration:

Consider a function g(x), such that

{eq}g(x) = \int_{a}^{b}\left | f(x) \right |dx {/eq}

To evaluate g(x), we need to find the interval ranging from a to b in which f(x) is positive and negative.

{eq}\displaystyle *\int x^a dx = \frac{x^{a+1}}{a+1} + c \quad \left[ \text{c is the constant of integration} \right] \\ *\int \cos x dx = \sin x + c \\ * \int_{a}^{b} f(x)dx + \int_{b}^{c} f(x) dx + ..... + \int_{y}^{z} f(x)dx = \int_{a}^{z} f(x)dx {/eq}

Answer and Explanation: 1

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{eq}\displaystyle a)\int_{-1}^{1} |2x-1|dz\\ b) \int_{0}^{\frac{3 \pi}{4}} |\cos x|dx {/eq}


Notice that the integration variable in...

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Learn more about this topic:

Definite Integrals: Definition


Chapter 12 / Lesson 6

A definite integral is found as the limit between a line graphed from an equation, and the x-axis, either positive or negative. Learn how this limit is identified in practical examples of definite integrals.

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