S₁ 2 63 Evaluate: A 16 B 105 C) None 16″ D 105 2π E 63 sinxcos³xdx is equal to

Q: 3x5 Evaluate S 3x4+6x33x2 - 6x O x2−2x +In 2 x²-2x-In O x² - 4x 2 O x² - 4x 2 -dx, using method of…

A: Integration

Q: π 5л Find the area bounded by the trigonometric curves y=sinx and y=cosx from x = - to x = 4 4 (A)…

A: See the details solution in below

Q: Where does the line through (-3, 1, 0) and (−1, 3, 8) intersect the plane 2x + y − z = -2? (x, y, z)…

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Q: 17. fe-Inx √√In x² dx 3

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Q: The volume of the solid generated by revolving the region bounded by x2= 4y and y2=4x about y=4 is…

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Q: For x 1/2 -dx and using the substitution u=x 1/2, the resulting integral takes the form: x-x 4u -du…

A: We can rewrite the given integral by using this substitution u = x1/2

Q: Find the cross product a x b. a = (7, 6, -5), b = (2, -1, 1) Verify that it is orthogonal to both a…

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Q: ad Find the equation of the tangent line to the graph of the given function at the given value of x.…

A: We have to solve the trangent line y

Q: Find the area bounded by the curve y=-x³ 1 - 16 A 8 square units B 16 square units 10 square units 4…

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Q: Find ·S= y dy 0(√3+2-5) (5√3+2-1+24)+C 0² (√y+2-5)(-5√/y+2+y+21)+C 03/(√3+2-5) (5√y+2+y+21) +C…

A: On solving this we will get

Q: Question 14 Find the area bounded by the curve y = - -x 16 A 10 square units B) 4 square units C 8…

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Q: 2. 2 4 Scot² 3x csc + 3xdx

A:

Q: y dy Find S- y+2 A ²/(√x+2-5)(-5√/y+2+y+21)+C ℗ ²/(√3+2-5) (5√/y+2-y+24) + C B Ⓒ(√x+2-5)…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: d) A scalar equation of a line that goes through T(2, -5) and is perpendicular to the line 3x - 6y =…

A: The given line is: 3x-6y=5⇒6y=3x-5⇒y=3x-56⇒y=12x-56 which has a slope m=12.

Q: The volume of the solid generated by revolving the region bounded by x²=4y and y2=4x about y=4 is to…

A: Follow the procedure given below.

Q: Question 18 Find - y dy (y + 2 A(√y+2-5) (5√/y+2+y+24)+C А Ⓡ(√y+2-5)(-5√/y+2+y+21)+C B Ⓒ(√3+2-5)…

A:

Q: substitutionu +5=√y+2. -5√/y+2+y+21)+C 5√y+2=y+24)+C

A: We have to choose the correct option from the given options according to the given information

Q: 5. Evaluate , x dV where S is the region (solid) bounded by x = 0 and x =

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Q: A ²/ (√x+2-5) (5√y+2+y+21) + C 3

A:

Q: Consider J x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)? (A) 1/2…

A: We have to find the integral

Q: aluate A B Ⓒ D Stan™ tan" (x) sec¹x dx. 1 M+2 - 777 +1 - tan tan (m + 1)(x) + tan (m + 1)(x) -tan…

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Q: 4. t²dt /t° +1 3√/₁³

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Q: x dx can be transformed to which of the following using trigonometric substitution? x²-1-1 x² + cose…

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Q: b The volume of the solid generated by revolving the region bounded by x2= 4y and y2=4x about y=4 is…

A: Volume of revolution

Q: Integrate each of the following. Show complete solution. 1. 1000dx 2. S²x¹ + 3x² + 1)dx 3. f(u² + u…

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Q: If s t5 - 10t², when will the acceleration d² s dt² O2 seconds O 0.5 second O 1.5 seconds 1 second…

A:

Q: Exercises To Solve [NO.5] D "Cosx dx. Sinx+25inx+5 6 3 b

A:

Q: 7. Use cylindrical coordinates to evaluate S √x² + y² dx dy dz where S is bounded by Z= √√x² + y², z…

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Q: Question 12 Consider ·S S(x-1 x-m+ (A) 17/6 B) 14/3 6 D) 5 3x5 3x4+6x²-3x² - 6x A B C + -+ x-1 x+1…

A: Consider ∫3x53x4+6x3-3x2-6x dx. Using the method of partial fractions, the given integral can be…

Q: 3x5 3x4+6x33x2 - 6x + In Evaluate S Ox²–2x (x-1) 1/6(x+2) 16/3 (x+1) 1/2 2 Ox²-4x (x-1) 1/6(x+2)…

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Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.1 cm/min.…

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Q: The volume of the solid generated by revolving the region bounded by x²=4y and y² = 4x about y = 4…

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Q: x² - 16 to fill in the table: - 4 5 4.5 4.1 4.01 Based on ONLY the table of values above, what…

A:

Q: QUESTION 10 Consider O 5 14/3 O 6 O 17/6 3x5 3x4+6x3-3x2 - 6x Sx-m + A+ dx Using the method of…

A: On solving this we will get

Q: To evaluate x²cosx dx' use integration by parts. What is the expression after the second integration…

A:

Q: The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x about y = 4 is…

A:

Q: QUESTION 12 x 1/2 ·S For S S- S- dx and using the substitution=x1/2, the resulting integral takes…

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Q: Consider √(x-m. 3x5 -dx. Using the method of partial fractions, the given integral can be written as…

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Q: Consider fx sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)? O 1/4 1 O…

A:

Q: Evaluate Ss sin (Inx) dx. Integration by parts will be used repeatedly. What is the expression after…

A:

Q: Stan" (x) sectx dx -tan (m + 1)(x). _¹_ -tan (m-1)(x) + C m+1 m-1 ¹__tan (™ + 2)(x) + —tan” (x) + C…

A:

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)2=2y, the…

A: Please see the below picture for detailed solution.

Q: The integral O 01 °: June 8 ° sec³ 4 can be transformed to which of the following when trigonometric…

A: Answer is (A)

Q: [sin(mx) cos(nx) dx 9. Suppose m and n are constants and m #n. Evaluate 1 1 -cos(m− n)x+ -cos(m+n)x…

A: Evaluate the integral

Q: The volume of the solid generated by revolving the region bounded by x²=4y and y2=4x about y=4 is to…

A: Washer Method

Q: Exercises To Solve [No.5] 6 "Cosx dx. Sin²x+25inx+5

A: Here is the solution

Q: To evaluate (A) (B resti x²cosx dx use integration by parts. What is the expression after the second…

A: In this question, we need to evaluate the given integral using integration by parts.

Q: 20. [(x²+2x-10/3 (5x+5)dx

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Q: The rate of growth of a population after t years is given by the equation P(t) = 5t. What is the net…

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Q: Evaluate A B fsir sin (Inx) dx. Integration by parts will be used repeatedly. What is the expression…

A: