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3 years ago

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Nookie1986 [14]3 years ago

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Answer:

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U-substitutions only work for specific kinds of expressions. Below, you are asked to choose a value of n for which u-substitutio

Dahasolnce [82]

Answer:

Step-by-step explanation:

(a) $\int x^n e^{5x^4+1} \ dx$

Suppose $5x^4 + 1 = f$

by differentiation;

$\implies \ 20 x^3 dx = df --- (1)$

Suppose n = 3

Then, the integral

$I = \int x^ 3 e^{5x^4 + 1} \ dx$

$= \int e^f \ \dfrac{df}{20}$

$= \dfrac{1}{20} \int e^f \ dt$

$= \dfrac{1}{20} e^f + C$

recall that $f = 5x^4 + 1$

Then;

$\mathbf{ I = \dfrac{1}{20}e^{5x^4+1}+C}$

(b) $\int \dfrac{cos (\dfrac{1}{x^3})}{x^n } \ dx$

suppose; $\dfrac{1}{x^3} = f$

$x^3 = f$

$\implies -3x^{-4} \ dx = df$

$\implies \dfrac{1}{x^4} \ dx =-\dfrac{1}{3} df$

If n = u, then the integration is:

$I = \int \dfrac{1}{x^4} \ cos (\dfrac{1}{x^4}) \ dx$

$= \int -\dfrac{1}{3} \ cos \ f \ df$

$= -\dfrac{1}{3} \int \ cos \ f \ df$

$= -\dfrac{1}{3} \ sin \ f + C$

Since; $x^3 = f$

Then;

$\mathbf {I = -\dfrac{1}{3} \ sin \ \Big( \dfrac{1}{x^3}\Big) + C}$

(c) $\int \dfrac{x+n}{x^2 + 8x -4} \ dx$

Suppose $x^2 + 8x - 4 = f$

Then, by differentiation of both sides

$(2x + 8) \ dx = df$

$(x + 4) \ dx = \dfrac{1}{2} \ df$

Suppose n = 4 in integration, then:

$I = \int \dfrac{(x + 4) }{x^2 +8x -4} \ dx$

By substitution;

$I = \int \dfrac{1}{2}\dfrac{1}{f} \ df$

$= \dfrac{1}{2} \ \ { In |f|} + C$

$\mathbf{= \dfrac{1}{2} \ \ { In |x^2+8x -4|} + C}$

7 0

3 years ago

What is m when 3m + 5 = 8

iren [92.7K]

Answer:

1

Step-by-step explanation:

If 3m + 5 = 8

We can say 8 - 5 = 3m

So, 3 = 3m

So, m = 1.

1 x 3 = 3!

7 0

3 years ago

Read 2 more answers

5. Suppose you choose a marble from a bag containing 3 red

makvit [3.9K]

Answer:

15/64

Step-by-step explanation:

Given

Red, R : 3 marbles

Blue, B : 5 marbles

Total : 5+3=8 marbles

If first marble is returned

P(Red) = 3/8

P(Blue) = 5/8

P (Red then Blue) = 3/8 x 5/8 = 15/64

8 0

4 years ago

Marc commutes to work on his bicycle, which has tires that measure 26 inches in diameter. A device on his bike informs him that

kykrilka [37]

the answer is > 31,692 in

6 0

3 years ago

Find square root of 128881 by division method

n200080 [17]

I thinks it 833/5000

7 0

3 years ago