12) Evaluate the following: (a) Evaluate the definite integral: f¹(7 √x + 3x • √x) dx (Leave answer in exact values, do not use decimal approximations.) (e) Evaluate the definite integral using the Evaluation Theorem. ST/A -π/4 1-sin² x dx

Q: 16. Use substitution to find and evaluate the definite integral. Give your answer in exact form. T/3…

A:

Q: Evaluate the definite integral. sin(2t)dt

A: we use substitution method

Q: D) Calculate the following definite integral: [* (/{√x - 1) dx

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Q: 2- Solve the equation for x : Cosh x = Sinh x +1/2.

A: We need to find out the value of x. The given equation is Cosh x=Sinh x+12 Now,  Cosh x=ex+e-x2  and…

Q: Find the indefinite integral using an appropriate trigonometric substitution and showing a right…

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Q: sin (r) -dr. R nvoke to integrate even powe

A: An integral is given by, I = ∫Rsin2xx2dx. The objective is to evaluate and state the identities that…

Q: Differentiate the function.  f(x)=cos{sin(tan(pi*x))}1/2

A: Given f(x)=cos{sin(tan(pi*x))}1/2

Q: Q5: Find for the following functions: (4) y = x sinh 2x-cosh 2x (2) y = tan³√cot(7x) ; (3) y = sin²…

A: Sol:- (2) ddxtan3cot7x Apply the chain rule =3tancot7x2ddxtancot7x

Q: Differentiate the given function. y=XV8X-5 y'= (Type an exact answer, using radicals as needed.)

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Q: Find for the following functions: (4) y = x sinh 2x --cosh 2x (2) y = tan³√/cot(7x); (3) y= sin Imvr

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Q: sin x-1 x+cos x -dx

A: