Use the formula f(x)g (x)dx = f(x)g(x) – ff (x)g(x)dx for the integration by parts, and Integrate h(x) = ſ(3 – 6 x) e(8x) dx in two steps. Identify f(x) and g(x) for the integral above defined by h(x). f(x) = g(x) =

Q: Suppose that fx cos(x²)dx = G(x) + C = F(x). Determine the constant of integration C if F(0) = 2. 0…

A: Given Integral  ∫xcos( x2 )dx∫xcos( x2 )dx = G( x ) + C Given condition F( 0 ) = 2

Q: 3x Let f(x) := 32 Select all of the following properties that f: A → B satisfies, when A = 2Z and B…

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Q: Determine the constant of integration of f (x)= ƒ (15xª – 3x²) da if f (1) = 4? O None of the…

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Q: Find 4 [3f (x) – g(x)]dx = i if 4 4 |r)dx = 4 and g(x)dx = 20

A: This question is related to definite integration, we will solve it using given information.

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Q: Calculate the definite integrals (a) I₁ =¹7 (2x − 1)(x + 2) dx - 18 (b) I₂ =2₂¹8 (x + 2)(√√x - 2) dx

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Q: (a) 18 d.x x² – 49 (b) 20 1 - dx 2x2 – 72 (c) 6. - dx x² – 4x – 5

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Q: Find [2f(x) – g(x)]dx = i if f(x)dx = 4 and g(x)dx = 50

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Q: 1. Basic Integration a. fx(x + 1)dx b. S √ √x+x² dx x C. √₁²|x-1|dx

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Q: Give an expression for p (x) so the integral p(x) cos(7x) dx can be evaluated using integration by…

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A: This is question of calculus  Here one equation is given  We have to decompose  it by apply both…

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A: 2a) From x=0 to x=1 there is a triangle of base=1 and height =1  So we have to find the area of the…

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Q: Use the reduction formula: [(In 2)" dx = 2(In x)" — n f (In 2)¹-1, times. First application of the…

A: Given: ∫(ln x)n dx=x(ln x)n-n ∫(ln x)n-1 dx     ........(1) By using the above result we have to…

Q: - 1) (2r + 1)½ (4x – 1) dx Perform the Integrations

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Q: Given f (x) = x – z² + 1 %3D - defined over the interval [0, 6]. Use integration methods to solve

A: (a) The interval [1.5, 5] is divided into 8 points, so the 8 points are (1.5, f(1.5), (2, f(2)),…