Question

Very Easyyy.x%20%3D%20..." id="TexFormula1" title=" \displaystyle\int^{ - 1}_{ - 4} (7x + 2)dx = ..." alt=" \displaystyle\int^{ - 1}_{ - 4} (7x + 2)dx = ..." align="absmiddle" class="latex-formula">

50point. ​

Answer 1

Answer:

x iş 5

Step-by-step explanation:

because -- is plus then 75 plus 2 is 77

Answer 2

Hello HayabusaBrainly!

$\huge \boxed{\mathfrak{Question} \downarrow}$

$\displaystyle\int^{ - 1}_{ - 4} (7x + 2)dx = ...$

$\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}$

$\int _ { - 4 } ^ { - 1 } ( 7 x + 2 ) d x$

Evaluate the indefinite integral first. We'll get it as..

$\int 7x+2\mathrm{d}x$

Now, integrate the sum by each term.

$\int 7x\mathrm{d}x+\int 2\mathrm{d}x$

Factor out the constant in the terms.

$7\int x\mathrm{d}x+\int 2\mathrm{d}x$

We know that, $\int\:x^{k}dx$ will be equal to $\dfrac{x^{k+1}}{k+1}$ where $k\bcancel{=}-1$. So, let's replace $\int\:xdx$ with $\dfrac{x^{2}}{2}$. Now, multiply 7 with $\dfrac{x^{2}}{2}$.

$\frac{7x^{2}}{2}+\int 2\mathrm{d}x$

Note that by using the table of common integrals rule we can see that $\int\:adx = ax$. So, $\int\:2dx = 2x$.

$\frac{7x^{2}}{2}+2x$

The definite integral is the anti-derivative of of the expression which is evaluated at the upper limit of the integration minus the anti-derivative of of the expression which is evaluated at the lower limit of the integration. So..

$\frac{7}{2}\left(-1\right)^{2}+2\left(-1\right)-\left(\frac{7}{2}\left(-4\right)^{2}+2\left(-4\right)\right)$

Now, simplify it...we'll get the answer as..

$\large\boxed{ \boxed{ \bf \: -\frac{93}{2}=-46.5}}$

__________________

Hope it'll help you!

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