Suppose that f and h are integrable and that: L f(x) = -1, f(x) dx = 5, h (x) dx = 4 , Find: %3D %3D a. -2 f(x) dx b. Sf) + h(x)] dx c. S f (x) dx d. 12 f(x) – 3 h(x)] dx e. S f(x) dx f.S,I h (x) – f(x)]dx Theorem

Q: 1 x, and the line perpendicular to 6 Find the area of a triangle bounded by the y axis, the line f…

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Q: (4)using the relation F= Vn show that J1(x) cos x %3D

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Q: Please

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Q: Find y as a function of x if x*y" + 11xy + 25y = x', y(1) = -4, y(1) = 0. y =

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Q: (b) Evaluate f, /2+ ]x| dx by method of substitution.

A: Break integral into two part then solve

Q: If L(f(x) – 2g(x))dx = 12 and g(x) = x, find f(x)dx. Hint: draw a sketch of g(x)! %3D

A: We have ∫28(f(x)-2g(x))dx=12g(x)=xWe have to find∫28f(x) dx

Q: If SeF dr = [c(-5x + 3y² ) dx + (x³y) dy, what is F? %3D F =

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Q: (늘 가 G-2). Find the value. A relative extrema of the function f occurs at f(x, y) = 9x2 + 3y2 - 9x +…

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Q: p) Determine | (hVx +r) dx (where h, r are real numbers).

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Q: Evaluate (3x²y + y)dx + (x³ +x) Select one:

A: Here we have to evaluate ∫(1,2)(4,5)3x2y+ydx+(x3+x)dy ............(1)  Here P(x,y)=3x2y+y and…

Q: Find the absolute extrema (max and min) of the function f(x) = ex 2−4 on [ -1,2]

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Q: The function f(x) = Ei-1 Cix;| is piecewise linear and convex. True O False

A: Step:- 1 Convex piece-wise Linear: - A function f: ℝn→ℝis a convex piece-wise linear if there exist…

Q: Find the line integral of F along the parabola y = x² from the origin to (4, 16).

A: Using green's theorem.

Q: . A function f(x) has the following properties: (=) de = 4, f(2)dz = 6, f(2)dz S r(2) dz = -2, […

A: a) We divide the integral into three subintegrals

Q: 1. = fVx*- Jーxa 4 %3D - 2. (x? +1)²(x+ 2)dx 2х-4 dx 3. V x-4x+1

A: 1. ∫x2-x4dx

Q: Differentiate the following function. 6x2 +5 y = x2 +1 dx (x² + 1)< dy (x² + 1) • : (6x² + 5) + (6x²…

A: You just need to apply quotient formula in order to solve this.

Q: 2 + Vx dx. (a) Evaluate 1 dx. x + x(ln x)2 (b) Evaluate

A: Explained below

Q: 2 f 2 f Consider the function f(x, t) = (x - ct)4+ (x + ct)4 where c is a constant. Calculate Əx²…

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Q: b) Evaluate f v1 – x² dx.

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Q: If feF - dr = Sc(4x + 4y²) dx + (x²y) dy, what is.

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Q: Draw the level curve for z = f(x, y) for each of the values listed below. Label each level curve…

A: Equating 2x2-y = z Equating with the values of z we can draw the graph for each function

Q: Evaluate F· dī where C F = = , and C is given by - T(t) = , 0 < t < T 0 <t<

A: Given