1. Calculate the Integral sin x cos x dx

Q: Determine the exact value of ex e3x cos 2x dx

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Q: 3. Evaluate (1+ sin x) dx.

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Q: Evaluate [sin³ a x cos x dx. + C

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Q: 5. Find the values of a and b such that dx tan 1 + sinx a + b . %3D

A: We need to integrate ∫11+sinxdx

Q: b. S dx cos2 x V9 + tan x

A: Using the substitution method and then find the given integration..... explanation of the solution…

Q: Calculate f 6 sinx cos² x dx.

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Q: Find for y = 5x sin x+ 10x cos x- 10 sin x. dx Dikdörtg

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Q: Classify and Solve dy cos x +y sinx = cosx dx

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Q: 5. Use substitution to find S sin1º0 cos 0 d0.

A: We will find the integration.

Q: Use the method of substitution to evaluate | 2x cos x? dx.

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Q: 3. Find S sin5 x cos* x dx.

A: Use substitution method

Q: 2 Ix sin'x COS X x² 2. (x sin?x? cos x? dx

A: ∫ xsin3x2cosx2dx

Q: Evaluate sin(9æ)cos(3x)dæ.

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Q: Show that COS x dx a² – x² sin a 2а where a is some positive number.

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Q: Verify. esc (x) [I-cos(2x)] = 2 sin (x) SC

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Q: Q57.a) Find if y=sin(tant) and t=cos(x) dx

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Q: Evaluate Jx/2 6 sin x (cos x + 1)³ dx

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Q: 2 Cos4 Sin (sinz) de

A: Consider the integral  ∫cosxsin2sinxdx

Q: sin x 6. Evaluate dx. 3 cos x

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Q: sin x dx 2+ cos x 4. - T

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Q: Find | cos? (πt) sin (π ) dr

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Q: B) Find and It x sin 3z and y= tan 3z dx

A: x=sin23xy=tan 3xWe need to find dydx and d2ydx2.

Q: dx It sin x-cos x COS

A: To evaluate:∫dx1+sinx-cosx Solution: We know,cos2x=1-tan2x1+tan2x     ...(1)sin2x=2tanx1+tan2x…