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Questions tagged [definite-integrals]

Questions about the evaluation of specific definite integrals.

A definite integral is defined as the area under a function from $a$ to $b$. Definite integrals sometimes involve calculating the indefinite integral, which is a function giving the area from $0$ to any $x$. However, definite integrals are most often separate from indefinite integrals in that the indefinite integral may not exist on its own. This is usually in the case of piece wise functions that are split along certain key points or integrals involving asymptotes.

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A small question about integrals

so I didn't find an answer online, so I would like to ask which answer is correct: $$\int_{-4}^4 x^3 \,dx = 0 $$ or $$\int_{-4}^4 x^3 \,dx = 64 $$ Thank you!
Qemikal
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Find the integral from the image given below

Equation problem click here $$\frac{d}{dx} \int_{x^4}^{x^3}\cos\left(t^3+t\right)\space{dt}= \;?$$ Does anyone know how to solve this problem??
user524460
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How to solve for $y$ in $\int_{0}^{y} \frac{A + t}{B-t} dt = N$

Is there a solution to definite integral $$\int_{0}^{y} \frac{A + t}{B-t} dt = N$$ Where $A$, $B$, $N$ are constants.
pavybez
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Definite integration integration by parts

Evaluate the integral $$\int_0^1\frac{x^7-1}{\log (x)}\,dx $$ [1]: https://i.stack.imgur.com/lcK2p.jpgplz I'm trying to solve this definite integral since 2 hours. Please, I need help on this.
Pranab Singh
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Solving this difficult integral with trigonometric functions.

Solve $$\int_{\pi/3}^\pi \cos\frac{1}{\sin(\csc x)}\cdot\cos(\csc x)\cdot\frac{\cos x}{\sin^2x\cdot\sin^2(\csc x)}\ dx$$ How to start. First simplify trigonometrically then differentiate? then it is more of a trigonometry question Or substitute…
user12345
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How to solve this integral and have a result in term of arccos?

This is the integral in order to made some approximation after the result. I need the result in term of $\arccos$. $$ \int_l^k\! \sqrt{\frac{R}{r} -1} \:\mathrm{d}r = \cos^{-1} (...). $$
physnolimits
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Assuming that $F(x)$ is continuous ,what is the derivation of integral

Assuming that $F(x)$ is continuous ,what is the derivation of $$\int_{1}^x (x^2+f(t)) \,dt \;?$$ we know that answer is not $x^2+f(x)$.
Mansi
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