Problem 1. Solve these integrals using substitution (a) [ x(x r(x - 2)5dx, (b) [te²³² test dt.

Q: Newton’s Method can be used to compute reciprocals without performing division. Letc > 0 and set…

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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: Find g(x) if g (x) = (30x² – 60x) - 75»²–15z² and g(0) = -3. Round any numbers to 4 decimal places…

A: We use substitution method

Q: 2. Without specifically finding its roots, show that f(x) = 0 for some x E [1, 2] where x2 4 f(x) =…

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Q: πχ If f(x) = 1 + x³ + tan 4 find (ƒ-¹)'(3)=?

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Q: 1. Evaluate: a) S x³ sec-1(ln (x)) dx

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Q: QUESTION 4 Solve the following integral by using substitution method. S(6- sin3x)' cos 3x dx.

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Q: Suppose ƒ is an even function with integralEvaluate each integral.

A: Given:           f  is  an even function.    ⇒  f(-x) = f(x)   for all x

Q: 1- x² tx

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Q: 1. Using the Modified Secant Method, find the highest real root of f(x) = 5(sin(x)) e* -1. Continue…

A: The given problem is to find the approximate root of given function using modified secant method…

Q: 1. (a) Show that 2e6x S- =dx can be reduced to a Table Entry, then finish the problem. √16-ex

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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: 3. Solve for fe)(r) given that f(r)% = sinh(3r)

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Q: a)If f(x) = x2 − 4x + 5, x ≥ 2; find a formula for the inverse function and write its domain.

A: Since multiple questions are asked, we will solve only since a) is already solved. To get the rest…

Q: Problem 1. Solve these integrals using substitution (a) x(x-2)³ dx, (b) text² di dt.

A: The given integrals:a∫xx-25dxb∫te3t2dtWe will solve them using substitution.

Q: 1. Solve for the othogonal trasctories y =x²(1-cx)

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Q: [5] assuming the constant of integraton is zero. Show your solution is correct by taking the…

A: We need to solve integral.

Q: (3) ((x² – 5x)e*dx

A: To evaluate: I=∫x2-5xexdx

Q: (a) By using substitution method, evaluate (x²³ − 1)² dx.

A: The integral isTo determine: The solution of the integral.

Q: (f) / 10 x² (x² + 1)³/2 dx using the hyperbolic substitution = sinh(t). You may leave your answer in…

A: The given integral

Q: Question 2 Solve the following integrals by using appropriate substitutions. 4x a) dx 3x2 -1 b)…

A: We can solve the problem by substitute method.   NOTE :: As per our guidelines we are supposed to…

Q: dx (Solve it using integration by Rational fractions) sintx+cos4x

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Q: 2. Determine the real ro accurate to 4 decimal

A: 2. Given,            f(x)=tanh(x2-8)

Q: . Let h (x) = f (x) + g (x). Find a. h' (1), b. h' (3) , and c. h' (4).

A: Given Data: Function: h(x)=f(x)+g(x) The derivative of function h(x) with respect to x is,…

Q: I g(x) dx = 14, find [2x) + 49(x)] dx. If f(x) dx = 33 and

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