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Author Jonathan David Author of Fiction
Author Jonathan David
False Reality Publishing

Factoring Roots Before Definite Integration | The Hardest Part of Calculus is Algebra

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Sample from The Ultimate Crash Course Series
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Factoring Roots Before Definite Integration

Solve the Factored Equation

(2x+5)(x-1)=0

(2x+5)=0 \quad \text{or} \quad (x-1)=0

x=-\frac{5}{2} \quad \text{or} \quad x=1

Calculus Note

In calculus questions, factoring and solving algebraic equations often represents only a small portion of the overall calculus procedure, but these algebra steps are essential. Tedious algebra becomes instinctive with practice.

Apply the Limits to a Definite Integral

Using the roots a=-\frac{5}{2} and b=1, apply the power rule for definite integrals:

\displaystyle \int_{-5/2}^{1} x^{23}\,dx=\frac{1}{24}(1)^{24}-\frac{1}{24}\left(-\frac{5}{2}\right)^{24}

This step is not conceptually difficult, but the algebra can be tedious.

The hardest part of calculus is algebra.

Sample from The Ultimate Crash Course Series
This lesson is part of the Ultimate Crash Course bundle. Get the full collection at Payhip and access over 1,000 lessons and podcasts through theSTEMmajor.com. 





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