f is continuous, then show the integral from 0 to π of xf(sin(x)) dx = π/2 times the integral from zero to π of f(sin(x)) dx Hint: consider the substitution u = π − x and properties of sin

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A: Given problem:-

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A: Find the integral of sin^2 (x/2) dx with the bounds 0 to π.

Q: Use integration by parts to establish the reduction formula: Jx" cos x dx = x" sin x – n x"-1 sin x…

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Q: Evaluate the integral. dx 9-x2 O sin-1 cos 1*+c O cos Cos 7 O 2 2 cos'1를x*C Sin 1

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Q: Find the integral of 12 sin^5 x cos^5 x dx if the lower limit is O and the upper limit is T/2.

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Q: 7. Find the integral of the hyperbolic function below. 6 sin(x) cosh[cos(x)] dx

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Q: 4. Use the definition of integration to find (1+2x' ) dx , that is find lim f(x; )Ax

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Q: Evaluate the integral sin x dx (2 + 3 cos x)2

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Q: 7. Use integration by parts to prove that for any positive integer n, | cos"x dx = 1 cosn-1xx+ n - 1…

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Q: Use integration by parts to establish the reduction formula: Jx" cos x dx = x" sin x – n x*-1sin x…

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Q: Evaluate the integral. (Use C for the constant of integration.) sin (x) cos (x) dx 4.

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Q: Evaluate the integral. π f(x) dx   0   where    f(x) =    sin(x)    if  0 ≤ x <  π 2 cos(x)    if…

A: we need to evaluate the integral of πf(x).dx given that  f(x)=sinx if 0≤x≤π/2       cosx if π/2 ≤x…

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Q: use a geometry formula to find the exact value of the definite integral.  5 dx on interval[-2,6]

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A: This question is based on indefinite integral.

Q: Evaluate the integral of x cos 2x dx with limits form 0 to pi/2. (A) -3/4 B 0.75 C -0.5 D 1/2

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A: answer is in next step

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Q: Find the definite integral of sin x -dx 0 1+cos x

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Q: Find the indefinite integral ∫ [arctan(x/2)] / (4 + x2) dx

A: ∫arctanx24+x2dx Now put, arctanx2=t⇒11+x22·12=dtdx⇒11+x24·12=dtdx⇒44+x2·12=dtdx⇒24+x2=dtdx⇒14+x2…

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Q: Find the antiderivative of f(x) = point (0,3). O F(x) = tan¹x +1 O F(x) = 2 tan ¹x +1 -1 O F(x) =…

A: Given: fx=24x2+1 and x,Fx=0,3   As we know the expression for the antiderivative; Fx=∫fxdx And…