Integrate the function $\sqrt{5+4x-x^2}$ from $4$ to $4$

Step-by-step Solution

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Final answer to the problem

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Step-by-step Solution

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  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Integrate using trigonometric identities
  • Integrate using basic integrals
  • Product of Binomials with Common Term
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Rewrite the expression $\sqrt{5+4x-x^2}$ inside the integral in factored form

$\int_{4}^{4}\sqrt{-\left(x-2\right)^2+9}dx$
2

When the bounds of an integral are the same, the integral is going to be equal to zero because the is no area to integrate

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Final answer to the problem

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Function Plot

Plotting: $\sqrt{5+4x-x^2}$

Main Topic: Definite Integrals

Given a function f(x) and the interval [a,b], the definite integral is equal to the area that is bounded by the graph of f(x), the x-axis and the vertical lines x=a and x=b

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