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Find the integral $\frac{2\int_{-2}^{1} x\left(4-x^2-\left(x+2\right)\right)dx}{9}$

Step-by-step Solution

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Solution

Final answer to the problem

$-\frac{1}{2}$
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Step-by-step Solution

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Rewrite the integrand $x\left(-x^2-\left(x+2\right)+4\right)$ in expanded form

$\frac{2\int_{-2}^{1}\left(2x-x^{3}-x^2\right)dx}{9}$

Learn how to solve problems step by step online.

$\frac{2\int_{-2}^{1}\left(2x-x^{3}-x^2\right)dx}{9}$

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Learn how to solve problems step by step online. Find the integral (int(x(4-x^2-(x+2)))dx&-2&12)/9. Rewrite the integrand x\left(-x^2-\left(x+2\right)+4\right) in expanded form. Expand the integral \int_{-2}^{1}\left(2x-x^{3}-x^2\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral of a constant times a function is equal to the constant multiplied by the integral of the function. The integral of a constant times a function is equal to the constant multiplied by the integral of the function.

Final answer to the problem

$-\frac{1}{2}$

Exact Numeric Answer

$-0.5$

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve integral of x(4+-1x^2)dx from -2 to 12/9 using partial fractionsSolve integral of x(4+-1x^2)dx from -2 to 12/9 using basic integralsSolve integral of x(4+-1x^2)dx from -2 to 12/9 using u-substitutionSolve integral of x(4+-1x^2)dx from -2 to 12/9 using integration by partsSolve integral of x(4+-1x^2)dx from -2 to 12/9 using trigonometric substitution

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Function Plot

Plotting: $-\frac{1}{2}$

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7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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