Evaluate the integral of I. I = 18 integral sin^5 x cos x dx.


Evaluate the integral of {eq}I {/eq}.

{eq}\displaystyle I = 18 \int \sin^5 x\ \cos x\ dx {/eq}.


The integral will be solved using the substitution method. The integral will become easy to evaluate and simpler and then after solving we will plug-in the values back in the integral.

Answer and Explanation: 1

To solve the integral we will use the substitution method

{eq}=18\int \sin^{5}x\cos xdx {/eq}

Using the substitution

Put {eq}\sin x=t\\ \cos xdx=dt {/eq}

Now plug-in the values back we get

={eq}18\left [ \frac{t^{6}}{6} \right ]+c {/eq}

Now by back substitution

{eq}=3\left [ \sin^{6}x \right ]+c {/eq}

Learn more about this topic:

Evaluating Definite Integrals Using the Fundamental Theorem


Chapter 16 / Lesson 2

In 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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