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3 years ago

Given that ∫51f(x)dx=1,∫53 f(x)dx=3 and ∫61f(x)dx=9 find ∫63 f(x)dx.

Mathematics

1 answer:

ELEN [110]3 years ago

6 0

$\displaystyle\int_1^6=\int_1^5+\int_5^6\implies\int_5^6=9-1=8$

$\displaystyle\int_3^6=\int_3^5+\int_5^6=3+8=11$

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Respuesta de (-0.5)²

Vladimir79 [104]

Answer:

0.25

Step-by-step explanation:

we have

$(-0.5)^2$

we know that

$-0.5=-\frac{1}{2}$

substitute

$(-\frac{1}{2})^2=(-\frac{1}{2})(-\frac{1}{2})$

Remember that

$(-1)(-1)=1\\(-1)(1)=(-1)$

$(-\frac{1}{2})(-\frac{1}{2})=\frac{1}{4}=0.25$

5 0

3 years ago

Find the values of a and b such that

Varvara68 [4.7K]

Answer:

a = 1.5

b = 1.75

Step-by-step explanation:

First, we need to solve $(x+a)^2$ and replace the result in the initial equation as:

$x^2+3x+4=(x+a)^2+b\\x^2+3x+4=x^2+2ax+a^2+b$

Then, this equality apply only if the coefficient of $x$ is equal in both sides and the constant is equal in both sides.

It means that we have two equations:

$3x=2ax\\4=a^2+b$

So, using the first equation and solving for a, we get:

$3x=2ax\\3=2a\\a=\frac{3}{2}=1.5$

Finally, replacing the value of a in the second equation and solving for b, we get:

$4=a^2+b\\4=1.5^2+b\\b=4-1.5^2\\b=4-2.25\\b=1.75$

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3 years ago