Evaluate the definite integral. esin (a) cos(x) d x

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Q: 9. The graph of f(x) = x* + 8x3 – 72x2 + 6 is concave down for A. -6 2 С. х< -6 D. -3 – 3/5 <…

A: The function id concave downward if f''(x)&lt;0

Q: dx 4 -sin e+C Using Trigonometric Substitution - = , express the answer in terms of x. (x² + x + 1)…

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Q: cos 2 dx O 32 -cos -5cos2 ()+7] + c 35 32 35 - cos(4)- 32 -cos) +c O 32 COS +C 스4

A: We have to find integral

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A: Given that the slope of the tangent line at any point (x,y) on a curve is 2x. So, dydx=2x=2(x12)

Q: | æ(5")dæ

A: topic - integration by parts

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Q: 6. S(x)= In(tanh 5"

A: As per bartleby guidelines we only give first question answers.

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Q: 4) y =iy ¡y' -x1

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Q: Integration by Parts In this case you will often be successful if you take u to be the function…

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Q: 9-x2 dx. - х x2

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Q: dx O 32 cos 35 스) -Scos ()+7] + c O 32 cos ()- -cos+c O 32 7 32 CO 5 32 cos 35 (즐) 5sin)+21+C

A: A detailed solution is given below

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A: We can solve as follows

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Q: Find any critical numbers of the function. (Enter your answers as a comma-separated list.) g(x) = x6…

A: For critical numbers, Put g'(x) = 0 and solve for x.

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Q: dx + (1 – x²)cot y dy = 0

A: Given problem :- dx + (1-x2 )cot(y) dy = 0 Find the general solution of given differential equation

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Q: ul = 7,0 = 25

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: (b) 1 When is the velociy of the particle positive? [0,1) U (3,4] When is it negative? (1,3) When is…

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Q: (æ² + 1)² x²ez² 2(x2 + 1) + C x²ez? 2(z² + 1) -ze +C O A Ов 1 2(x2 + 1) cea 2 2(2² + 1) - 2" +C…

A: The given integral is: I=∫x3ex2(x2+1)2dx=∫x2ex2(x2+1)2x dx Substitute x2=u⇒2xdx=du⇒xdx=du2 So,…