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Integrate the function $7-y^2-\left(y^2-11\right)$ from $-3$ to $3$

Step-by-step Solution

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Solution

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Final Answer

$72$
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Step-by-step Solution

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Rewrite the expression $7-y^2-\left(y^2-11\right)$ inside the integral in factored form

$\int_{-3}^{3}2\left(y+3\right)\left(-y+3\right)dy$

Learn how to solve definite integrals problems step by step online.

$\int_{-3}^{3}2\left(y+3\right)\left(-y+3\right)dy$

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Learn how to solve definite integrals problems step by step online. Integrate the function 7-y^2-(y^2-11) from -3 to 3. Rewrite the expression 7-y^2-\left(y^2-11\right) inside the integral in factored form. The integral of a constant times a function is equal to the constant multiplied by the integral of the function. Rewrite the integrand \left(y+3\right)\left(-y+3\right) in expanded form. Expand the integral \int_{-3}^{3}\left(9-y^2\right)dy into 2 integrals using the sum rule for integrals, to then solve each integral separately.

Final Answer

$72$

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 (7+-1y^2)dy from -3 to 3 using partial fractionsSolve integral of (7+-1y^2)dy from -3 to 3 using basic integralsSolve integral of (7+-1y^2)dy from -3 to 3 using u-substitutionSolve integral of (7+-1y^2)dy from -3 to 3 using integration by partsSolve integral of (7+-1y^2)dy from -3 to 3 using trigonometric substitution

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Function Plot

Plotting: $7-y^2-\left(y^2-11\right)$

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0
a
b
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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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Main Topic: Definite Integrals

Given a function f(x) and the interval [a,b], the definite integral is equal to the area that is bounded by the graph of f(x), the x-axis and the vertical lines x=a and x=b

Used Formulas

3. See formulas

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