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Solving: $\int_{0}^{x^2}\sin\left(t\right)dt$
Solve instead: $\int_0^{x^2}\left(sin\left(t\right)\right)dx$

Exercise

$\int_0^{x^2}\left(sin\left(t\right)\right)dx$

Step-by-step Solution

1

Apply the integral of the sine function: $\int\sin(x)dx=-\cos(x)$

$\left[-\cos\left(t\right)\right]_{0}^{x^2}$
2

Evaluate the definite integral

$-\cos\left(x^2\right)- -\cos\left(0\right)$
3

Simplify the expression

$-\cos\left(x^2\right)+1$

Final answer to the exercise

$-\cos\left(x^2\right)+1$

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
  • Load more...
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$\int_0^1\left(\frac{x}{1-x^2}\right)dx$

$\int_0^1\frac{dx}{\left(x+1\right)\left(x^2+1\right)}$

$\int_1^2\frac{1}{x\cdot\left(x+1\right)}dx$

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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