3. Find the average value of the function on the given interval.

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: A trough is full of liquid of weight density 9,000 N/m³. The ends of the trough are equilateral…

A: We need to setup integral.

Q: To evaluate x²cosx dx' x2sinx+2x cosx – 2 x2sinx+2x cosx – 2 x²sinx- – 2x cosx — 2 x2sinx – 2x…

A:

Q: Question 9 The volume of the solid generated by revolving the region bounded by x²=4y and y2=4x…

A: Solution is here

Q: y dy Find S² using the substitution u +5=√y+2. √y+2 (A) (√3+2-5) (5√3+2+y+21) +C 3…

A:

Q: 20. For A. B. C. D. S x1/2 dx and using the substitution u=x1/2, the resulting integral takes the…

A:

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

A:

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

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) 1/4 B)…

A:

Q: Find the area of the region lying between the inner and outer loops of the limacon r = 1 – 2 sin θ

A: Solution of the problem as follows

Q: (d) ƒ COS √1+sin x dx, (e) cos(lnx) S dx Т

A:

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

A:

Q: What is the solution to the following initial value problem? dy + 4x = 3 y(0) = 1 da Oy=-2x² + 3x -…

A:

Q: Question 17 1/2 S. dx and using the substitution = x 1/2, the resulting integral takes the form:…

A:

Q: A spherical tank of diameter 4 m is half-full of water (weight density = 9800 N/m³). Setup the…

A:

Q: dx can be transformed to which of the following when trigonometric substitution is used? (x²+4)²…

A: Integration by Trigonometric substitution.

Q: The volume of the solid generated by revolving the region bounded by x²=4y and is to be solved using…

A:

Q: Evaluate 1 m+3 1 m+ 1 I M+2 T }}}+1 tan" (x) sec¹x dx I -tan (m + 3) (x) + m+1 1 -tan (m + 1)(x) +…

A: SOLUTION-

Q: y dy Find 13 using the substitution +5=√y+2. √y+2 A ²/ (√x+2-5) (5√/y+2-y+24) + C 3 B (√9+2-5)…

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: -S- A Ⓡ / T B C S (D) S- For x1/2 dx and using the substitution u=x¹ x1/2, the resulting integral…

A:

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

A:

Q: S= Evaluate Ox² - 4x 2 Ox²–2x 2 O x² - 2x - In x² - 4x 2 3x5 3x4+6x + In 3x² - 6x - (x-1) 1/6(x+2)…

A: Explained below

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

A:

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

A:

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

A:

Q: What is the value of f(1) - 16B in I x³ Inx dx = f(x) ( (1/4) Inx - B) + C? 01 3 00 02

A:

Q: Evaluate sin (Inx n(Inx) dx xsin (Inx) + xcos (Inx) - [sin (In x) dx+C _xsin (Inx) – xcos (lnx) –…

A:

Q: Evaluate tan" (x) sec4x dx. 1 ¹__tan (m + 1)(x) + ___¹__tan (™− 1)(x) + C A. m+1 m-1 1 1 -tan (m…

A:

Q: 4 b. [√x ln xdx, 1 4 ㅠ C. fx√4-xdx, d. fx sin (2x) dx. 0

A: Solve the following

Q: Find 36 zdV, where E is the solid tetrahedron with vertices (0,0,0), (3,0,0), (0,6,0), and (0,0,2) E

A:

Q: 1. Consider [x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)? A. 3/8…

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 B)…

A:

Q: -x² 9 d. f (x) = xe [0, 5]. e. f(x) = |x² − 4], [0,3]. sin x f. f(x) = = [-ㅠ -π, π]. x² + 1

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Evaluate A B с D S= 3x-5 3x4 + 6x3-3x2 - 6x x² - 4x 2 x² - 2x 2 x² - 4x 2 x2-2x-In (x-1) 1/6(x+2)…

A:

Q: Find the area bounded by the trigonometric curves y=sinx and 2.828 square units 1.414 square units…

A: Given that curve y=sinx and y=cosx    from x=π4 to x=5π4To find :Area bounded by the region from…

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

A:

Q: What is the value of f(1) - 168 in x³ Inx dx = f(x) ((1/4) Inx-B) + C? 0 2 0 3 01

A:

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

A: using circular ring method evaluate the volume

Q: ·S- The integral x dx x²+√√√x²-1-1 can be transformed to which of the following using trigonometric…

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: Question 19 5x Find the area bounded by the trigonometric curves y=sinx and y=cosx from x=-to x=-…

A: Given

Q: Evaluate tan" (x) sec¹x dx A B © D -tan (m+3)(x) + ¹ -tan (m+1)(x) + C m+3 m+1 −tan (m +1)(x) — —_¹…

A: This question can be solved using the concept of integration by substitution.

Q: Question 13 The integral dx √(x²+4)² c'e ³0 do sin²0 de Ⓒ-csc³0 Ⓒos²0 csc ³0 de cos¹0 de can be…

A:

Q: Find the area bounded by the trigonometric curves y=sinx and y=cosx from; x== 3.459 square units…

A: Area bounded by the curve .

Q: An inverted pyramid is being filled with water at a constant rate of 50 cubic centimeters per…

A:

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: can be transformed to which of the following when trigonometric substitution is used? (x²+4)² sin ²0…

A: Please see the answer below.

Q: x dx x² + √√x²-1-1 The integral - (A) cose de can be transformed to which of the following using…

A:

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

A: