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3 years ago

Help my friend out?

Mathematics

2 answers:

IrinaVladis [17]3 years ago

5 0

Answer:

13. -2

14. 0

15. 2

16. 0

Step-by-step explanation:

Since the function is originally f(x), you go to wherever the x value is and see what the y value is.

So...

f(2) means go to x = 2 and see that y = -2

posledela3 years ago

3 0

13. -2
14. 0
15. 2
16. 0
hope this helps:)

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Please help me do it

Lana71 [14]

Step-by-step Explanation:

We are going to solve this problem using integration by parts. We can write the integrand as

$\dfrac{4x}{x^2+4x+3} = \dfrac{4x}{(x+3)(x+1)}$

$\:\:\:\:\:\:\:\:\:\:\:\:\:= \dfrac{A}{x+3} + \dfrac{B}{x+1}$

$\:\:\:\:\:\:\:\:\:\:\:\:\:= \dfrac{Ax + A + Bx + 3B}{x^2+4x+3}$

$\:\:\:\:\:\:\:\:\:\:\:\:\:=\dfrac{(A+B)x + (A+3B)}{x^2+4x+3}$

Comparing the above term to the left hand side, we can see that

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$\dfrac{4x}{x^2+4x+3} = \dfrac{6}{x+3} - \dfrac{2}{x+1}$

We can now easily integrate this expression as follows:

$\displaystyle \int{\dfrac{4x}{x^2+4x+3}}dx = 6\int{\dfrac{dx}{x+3}} - 2\int{\dfrac{dx}{x+1}}$

$\:\:\:\:\:\:\:\:\:\:\:\:\:= 6\ln|x+3| - 2\ln|x+1| + C$

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