Given dx dy 8x find y. x2-4 A. 8x In |x2 – 4| + c B. 8 ln |x2 – 4|+ c C. 4x ln |x2 – 4|+ c D. 4 ln |x2 - 4| + c С.

Q: Evaluate. 5 - 3 (7x + y) dx dy 0 - 4 5 - 3 I (7x+ v) dy dy i (Simplify v

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Q: 2. [2x(x²-1) dx 3. 4 √(2x² - 5x+3)( 21² 5x² + 3x) a dx 3 2

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Q: 1 315 y | 3/5 -1

A: To determine the slope of the given line.

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Q: |(x – 3) V/6x – x²dx b. TIn(x)dx с.

A: The given question as belonging to the calculus in which we have to find the value of the given…

Q: 3 dx = o 1+x

A: the given integral is ∫0∞x-231+xdx Rewrite the integral as ∫0∞1x231+xdx first calculate ∫1x231+xdx…

Q: 1 2x Evaluate [(4x-7)ay dx.

A: To evaluate: ∫01 ∫x22x (4x−7)dydx Let I=∫01 ∫x22x (4x−7)dydx First evaluate with respect to y taking…

Q: 1 (2x-3)4 4. S dx

A: Follow the procedure given below.

Q: xcos(2x) dx = None of these п/9 2n

A: We have: I= ∫ x cos(2x) dx Integrating by parts: ∫fg' = fg - ∫f'g Taking f= x and g'= cos(2x)  Thus,…

Q: 7x+6x+5 dx. Evaluate J(x+1)(x² +1)'

A: Consider the given integral.

Q: 1. . x + 4 dx x² + 5x – 6

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Q: dy dx for A B y=23√x²-3arcsin(x³) True False 2 9x² 33/x /1-x6

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Q: X 3 x² e-x³ dx I

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Q: Find if x = and y = t +3 (t+1) 1 %3D dz O a. none of these O b. (t+1)°(4t + 3) Oc름(t-1)°(4t-1) O d.…

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Q: Find dy/dx if y = 3(x² − 2x)(6 + x5). O 21x6-36x5+ 36x - 36 21x6 + 36x5 + 36x - 36 O 21x6-36x5 + 36x…

A: Solve for the differentiation

Q: b. √x+√9-5x²dx

A: Topic:- integration

Q: d 3 Evaluate dx √√In(6 - x²) at x = 1.

A: −15ln(5)32​2​Explanation:

Q: Find 5 f" 19 xif [ 15 xx 16 f(3x + 4) dx if Enter the exact answer. f (x) dx = 1.

A: To find the value of given definite integral

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Q: d Find dx 0.4 - 2 - 3.7x + 8x d 0.4 - 3.7x - 2 + 8x = dx

A: SOLUTION-

Q: | f(x)dx = 3 and f(x)dx = 7 , then (2f(x) +3)dx = If 4

A: TO FIND ∫43(2f(x) +3) dx GIVEN - ∫03f(x) dx = 3 ∫04f(x) dx =7 USE THIS PROPERTY TO SIMPLIFY- ∫abf(x)…

Q: Eliminate the arbitrary constants. y ln y = Ae* + Be¯x

A: We have to eliminate the arbitrary constants A and B from ylny=Aex+Be-x

Q: √ 1 x²√2x-x² dx = x+¹√ √√2x-x² + c 3x²

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Q: Evaluate. 17x - 19 √(x + 5) (22² + 1) dx = (Use c for the constant of antidifferentiation)

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Q: 3. = Cos xsin +xax+a 5/2 3/2 1. Ans: Y= 4sin'x* sinx+ To CAx+4)^- Cax+a) 3.

A: To solve: dydx=cos3x sin2x+x2x+1 Solution Given differential equation can be written as: dy=cos3x…

Q: Complete the table below by finding the product of each x-value times its corresponding y-value. For…

A: Given data:   Temperature (°C) x Solubility (g/100mL) y 10 31 20 33 30 37 40 41 50…

Q: f 2³x dx = O 0 23x In 2 + C ○ 23x+1 + C 3x+1 23x In 8 0 23x ln 2 O + C + C

A: To evaluate: I=∫23xdx

Q: dx Evaluate 2 -1 O -2 O -0 O O O O

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Q: 2f(x)dx = - 4 and | (F(x) + 1)dx =7. Then | (3f(x) – 2x)dx = Select one: а. -2 b. 19 С. 10 d. 13

A: ∫-122f(x)dx=-4 and ∫-13(f(x)+1)dx=7. find ∫23(3f(x)-2x)dx

Q: dx 43. Evalua Jx +2)(x² +4x + 10) te

A: To simplify this integral, we use partial fraction decomposition. Thus,…

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Q: Find zα/2 for α=0.19.

A: Given: α=0.19

Q: 2.2 (x²-y² + sxy + 2) y.dx + ( x + ² + 4xy + 2)x.dy=0

A:

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.