Solve the system of equations 2x-y=1; x+2y=8 graphically and find the coordinates of the points where corresponding lines intersect y-axis.
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Find the integral value
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$- \dfrac {x + 1} {e ^ {x}} + C$
Using partial integration
$\color{#FF6800}{\int xe ^ {- x}dx}$
$ $ To solve the integral, substitute $ v = - e ^ {- x} $ and $ u = x $ , and use the partial integration formula $ \int udv = uv - \int vdu $ $ $
$\color{#FF6800}{x \times (- e ^ {- x}) - \int - e ^ {- x}dx}$
$\color{#FF6800}{}x \times (- e ^ {- x})\color{#FF6800}{ - }\int \color{#FF6800}{- }e ^ {- x}\color{#FF6800}{}dx\color{#FF6800}{}$
$ $ Utilize integration $ \int - f(x)dx = - \int f(x)dx $ $ $
$\color{#FF6800}{}x \times (- e ^ {- x})\color{#FF6800}{ + }\int e ^ {- x}dx\color{#FF6800}{}$
$\color{#FF6800}{}x \times (- e ^ {- x})\color{#FF6800}{ + \int e ^ {- x}dx}$
$ $ Using $ \int e ^ {- x}dx = - e ^ {- x} $ , calculate the integral $ $
$\color{#FF6800}{}x \times (- e ^ {- x})\color{#FF6800}{ - e ^ {- x}}$
$\color{#FF6800}{x \times (- e ^ {- x}) - e ^ {- x}}$
$ $ Solve the formula $ $
$\color{#FF6800}{- \dfrac {x + 1} {e ^ {x}}}$
$\color{#FF6800}{- \dfrac {x + 1} {e ^ {x}}}$
$ $ Add integral constant $ C \in ℝ $ $ $
$\color{#FF6800}{- \dfrac {x + 1} {e ^ {x}} + C}$
Solution search results
$18.$ The solution of the equation $2x+3$ $\left(x\right)-4$ $\left(-x\right)$ $=4\left(whe$ (where [x] and $\left(\times 3$ denote integral and fractional part of $X\right)$ lies in the $inteWa1:$ $\left(A\right)$ $\left(0,1\right)$ (B) $\right)$ $\left(1,2\right)$ $\left(C\right)\left(2,3\right)$ (D) None of these
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Find $y^{'}\left(x\right)$ at the point $\left(1$ $1\right)$ if $3^{x+lny}+2^{x^{2}-y}=4^{2y-x}$ .
10th-13th grade
Calculus
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