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Math
Indefinite Integration Topics

Indefinite Integration Questions

Find the general indefinite integral. (Use C for the constant Integration.)
∫(x^5)^1/4 dx

Math

Indefinite Integration Solutions

Find the general indefinite integral. (Use C for the constant Integration.) ∫(x^5)^1/4 dx

Find the indefinite integral. (Use C for the constant of integration.)
∫ eˣ√(1-e²ˣ) dx

Math

Indefinite Integration Solutions

Find the indefinite integral. (Use C for the constant of integration.) ∫ eˣ√(1-e²ˣ) dx

A small metal bar, whose initial temperature was 10° C, is dropped into a large container of boiling water. How long will it take the bar to reach 70° C if it is known that its temperature increases 2º during the first second? (The boiling temperatur

Math

Indefinite Integration Solutions

A small metal bar, whose initial temperature was 10° C, is dropped into a large container of boiling water. How long will it take the bar to reach 70° C if it is known that its temperature increases 2º during the first second? (The boiling temperature for water is 100° C. Round your answer to one decimal place.) How long will it take the bar to reach 96° C? (Round your answer to one decimal place.)

Math

Indefinite Integration Solutions

Find the indefinite integral. (Use C for the constant of integration.) ∫eˣ√(1-e²ˣ) dx

Evaluate the indefinite integral
∫41cos²(17x)dx

Math

Indefinite Integration Solutions

Evaluate the indefinite integral ∫41cos²(17x)dx

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u-substitution: defining u
Anna was asked to find
as
12.c
dx using u-substitution.
4x3 – 6
Ho

Math

Indefinite Integration Solutions

lit View History Bookmarks Window Help < khanacademy.org [ Presbyteria... A AP Calculus w/ Greenman oh Midi Dresses | Knee Length Dresses... Search X Khan Academy u-substitution: defining u Anna was asked to find as 12.c dx using u-substitution. 4x3 – 6 How should Anna define u? Choose 1 answer: © A u= 12x2 B U 1 4x3 6 © 1 U= u= 4.03 - 6 Stuck? Review related articles/videos or use a hint. $ 26 sty ER MacBook Air F2 80 Q F3 F4 F5 F6 &

u-substitution: defining u
Jake was asked to find
vo
6x2 cos(2x + 1) dx using u-substitution.
How should Jake define u?
Choose 1 answer:
u= 2x3 + 1
B
u =
cos(2x3 + 1)
C
u= 6x2
u = cos(x)
=
Stuck? Review related articles/videos or use a hint.
Report a po
Do

Math

Indefinite Integration Solutions

u-substitution: defining u Jake was asked to find vo 6x2 cos(2x + 1) dx using u-substitution. How should Jake define u? Choose 1 answer: u= 2x3 + 1 B u = cos(2x3 + 1) C u= 6x2 u = cos(x) = Stuck? Review related articles/videos or use a hint. Report a po Do 4 problems Oo 26 sty ill X

Deep dives!
9. The function is defined above. The
()
(B) 2
(A) -2
Group MC #7
Name:
No work, no credit. Hint: for the first one, factor a three out of the denominator (so there will be a 1/3 in front
of the integral) before any u-substitution
che =
3.2 + 1

Math

Indefinite Integration Solutions

Deep dives! 9. The function is defined above. The () (B) 2 (A) -2 Group MC #7 Name: No work, no credit. Hint: for the first one, factor a three out of the denominator (so there will be a 1/3 in front of the integral) before any u-substitution che = 3.2 + 12 (A) - 3 In I.t + 4 + c In l.+ + +1+c (B) (C) 3 In l. + 4 +C 3 In l.x + 4 + c w (D) dx = 7.15,"s(t ) dx = – 3 and s(t) dx = 5, then L686.x) dx (C) 2 (D) 8 (A) - 8 (B) - 2 2 ge la 2 yefix) rm A 9. The graph of a functionſ is shown above. Which of the following expresses the relationship between (A) Si sx) dx. (%(x) dx, and ('76x) dx ? r(s) de < (5(x) dx < (5(x) dx for (x) dx = f (x) dx < 11 (1) de 10 d. (x) de < 1 (1) de < for (a) de (D) ) de < 1*70x) dx < Pra) de (B) (<

Use the given transformation to evaluate the integral.
(x - 5y) da, where R is the triangular region with vertices (0,0), (5, 1), and (1,5). * = 5u + v, y = x + 5v
Need Help?
Read It
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Master it

Math

Indefinite Integration Solutions

Use the given transformation to evaluate the integral. (x - 5y) da, where R is the triangular region with vertices (0,0), (5, 1), and (1,5). * = 5u + v, y = x + 5v Need Help? Read It Watch It Master it

ET
Problem 3 (5 points). If we know that f'(x) = xe-rand f(0) = è, then which of the
following is the function f(x)?
(a) f(x) = {e-r-1
(b) f(1) = {e-r? - 1
(c) f(x) = -je-r' +1
(a) f(x) = -3e-4-1
(e) none of the above
2

Math

Indefinite Integration Solutions

ET Problem 3 (5 points). If we know that f'(x) = xe-rand f(0) = è, then which of the following is the function f(x)? (a) f(x) = {e-r-1 (b) f(1) = {e-r? - 1 (c) f(x) = -je-r' +1 (a) f(x) = -3e-4-1 (e) none of the above 2

1
A population of bacteria will grow at a rate given by w' (t) = (4 + 6), where w is the weight (in milligrams) after t hours Find the change in weight of the population from t=0 to t=4
Set up the definite integral that gives the change in weight of the po

Math

Indefinite Integration Solutions

1 A population of bacteria will grow at a rate given by w' (t) = (4 + 6), where w is the weight (in milligrams) after t hours Find the change in weight of the population from t=0 to t=4 Set up the definite integral that gives the change in weight of the population from t=0 to t = 4 years dt

$Evaluate s dx , for x>4, in two ways: using partial fractions and a trigonometric substitution. Reconcile your two 2 x - 16 answers. First evaluate S dx x? - 16 using partial fractions. Factor the denominator of the integrand. x2 - 16 = (x+4)(x-4) Using th$

Math

Indefinite Integration Solutions

Evaluate s dx , for x>4, in two ways: using partial fractions and a trigonometric substitution. Reconcile your two 2 x - 16 answers. First evaluate S dx x? - 16 using partial fractions. Factor the denominator of the integrand. x2 - 16 = (x+4)(x-4) Using the result of the previous step, rewrite the integrand using partial fraction decomposition. dx A B + dx X-4 |x+4| x - 16 Solve for A and B. 1 A= and B= 8 8 (Type integers or simplified fractions.) Substitute the determined values for A and B into the integrand from a previous step and integrate. dx X-4 s 1 In 8 + C X? - 16 X+4

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