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Exercise

$\int_4^{4.5}\left(e^{x^4}\right)dx$

Step-by-step Solution

1

Apply the formula: $\int e^{\left(a^b\right)}dx$$=\frac{Ei\left(a^b\right)}{\log \left(a\right)}+C$, where $a=x$ and $b=4$

$\left[\frac{Ei\left(x^4\right)}{\log \left(x\right)}\right]_{4}^{4.5}$
2

Evaluate the definite integral

$\frac{Ei\left(4.5^4\right)}{\log \left(4.5\right)}- \frac{Ei\left(4^4\right)}{\log \left(4\right)}$

Final answer to the exercise

$\frac{Ei\left(4.5^4\right)}{\log \left(4.5\right)}- \frac{Ei\left(4^4\right)}{\log \left(4\right)}$

Try other ways to solve this exercise

  • Choose an option
  • 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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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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