Compute the following integral. \int\limits_0^{{\pi \over 2}} {\left( {{e^{ - x}} + \cos x -...
Question:
Compute the following integral.
{eq}\int\limits_0^{{\pi \over 2}} {\left( {{e^{ - x}} + \cos x - \sin x} \right)} dx {/eq}
Definite Integrals:
Some facts related to the integrals are given below:
- We can compute the definite integrals only for the functions that are real-valued and continuous on the closed interval {eq}[a,b] {/eq}.
- The indefinite integral simply computes the antiderivative of any function.
- Moreover, on differentiating an antiderivative w.r.t. the independent variable, we can obtain the original function.
Answer and Explanation: 1
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To compute: $$\displaystyle \int\limits_0^{\frac{\pi}{2}} {\left( {{e^{ - x}} + \cos x - \sin x} \right)} \ \text dx
$$
$$\displaystyle...
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Evaluating Definite Integrals Using the Fundamental Theorem
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Chapter 16 / Lesson 2In calculus, the fundamental theorem is an essential tool that helps explain the relationship between integration and differentiation. Learn about evaluating definite integrals using the fundamental theorem, and work examples to gain understanding.
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