Definite Integral Calculator
Calculus
Intro: Computes exact values with FTC, careful bounds changes, and numerical checks when needed.
Worked example
- $\displaystyle \int_{0}^{\pi} x\sin x\,dx$
- Use integration by parts: let $u=x\Rightarrow du=dx$, $dv=\sin x\,dx\Rightarrow v=-\cos x$.
- $\int x\sin x\,dx= -x\cos x+\int \cos x\,dx=-x\cos x+\sin x + C$.
- Evaluate from $0$ to $\pi$: $\big[-x\cos x+\sin x\big]_{0}^{\pi}$.
- Plug in $\pi$: $-\pi\cos\pi+\sin\pi=-\pi(-1)+0=\pi$.
- Plug in $0$: $-0\cdot\cos0+\sin0=0$.
- Difference: $\pi-0=\boxed{\pi}$.
FAQs
Can it change bounds during $u$-sub?
Yes — or it will back-substitute if you prefer original bounds.
Why choose Mathix?
- Get clear, step-by-step solutions that explain the “why,” not just the answer.
- See the rules used at each step (power, product, quotient, chain, and more).
- Optional animated walk-throughs to make tricky ideas click faster.
- Clean LaTeX rendering for notes, homework, and study guides.
How this calculator works
- Type or paste your function (LaTeX like
\sin,\lnworks too). - Press Generate a practice question button to generate the derivative and the full reasoning.
- Review each step to understand which rule was applied and why.
- Practice with similar problems to lock in the method.