-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

Q: 3x5 S 3x4+6x³-3x2-6x x²-2x = 2 [ (x-1) 1/6 (x+2) 16/3 (x+1) 1/2 ® [ B x² - 4x 2 x-1) 1/6(x+2) 16/…

A:

Q: Estimate the slope of the tangent line to the curve at the given point (-0.5,4.998) on the graph to…

A: It is clearly seen in the figure that the tangent line is horizontal to the x axis at the point…

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

A: Explained below

Q: [x²cos x²cosx dx, use integration by parts. What is the expression after the second integration by…

A: We will use integration by parts to solve this question.

Q: What is the value of f(1) - 16B in I x³ Inx dx = f(x) ( (1/4) Inx - B) + C? 2 0

A: Given; ∫x3lnxdx=fx14lnx-B+C    ...(1)   First, we have to find the integral value. I=∫x3lnxdx Apply…

Q: Find 1- y dy y+2 using the substitutionu +5= √√y+2.

A:

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by , the x-axis, and…

A:

Q: For x 1/2 dx and using the substitution u=x1/2, the resulting integral takes the form: 4u -du 4-12…

A: We can solve the integral by using substitution .

Q: 19. The volume of the solid generated by revolving the region bounded by x²=4y and y2=4x about y=4…

A:

Q: QUESTION 7 Evaluate 3x5 3x4+6x³-3x² - 6x x²-2x-In O x²-4x 2 O x²-4x 2 O rẻ-2r 2 [(x-1) 1/6(x+2) 16/3…

A:

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

A:

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

A: We have to determine above integral

Q: O 15.21 square units 33.43 square units O 43.23 square units O 22.89 square units

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: Given :Region bounded by x2=4y and y2=4xRevolving about y=4

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

A: Given

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

A:

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

A: Given:         Density of Liquid ρ=9000 N/m3          Sides of triangle a=2 m     The expression for…

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

A:

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

A:

Q: . Given u = (-3,-4, -1), v = (6,2, -3), find (a) ||u|| (b) ||u+v|| u (c) u + v (d) u+v

A:

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

A:

Q: Suppose m and n are constants and m #n. Evaluate sin(mx) cos(nx) dx A − cos(m− n)x+ · -cos(m+n)x] +…

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

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: A ²/ (√x+2-5) (5√y+2+y+21) + C 3

A:

Q: Evaluate tan" (x) sec4x dx. 1 1 A -tan 2) (x). + (m+2 -tan" (x) + C m+2 m (m+1) ¹) (x) (m- m+1 1…

A:

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

A: Using circular ring method about y=4 find outer and inner radius then evaluate volume

Q: 3x5 ·S -dx- Using the method of partial fractions, the given integral can be written as 3x4+6x³3x² -…

A:

Q: Find the area bounded by the curve 16 square units 10 square units 4 square units 8 square units 16…

A:

Q: The integral O x dx can be transformed to which of the following using trigonometric substitution?…

A:

Q: Find the area bounded by the curve y = 1x³ - 2x² + 3x and the line x3_ 16 16 square units 10 square…

A:

Q: Л 5л nd the area bounded by the trigonometric curves y=sinx and y=cosx from x=- to x=-. 4 4

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: Question 3 Evaluate sin (Inx) dx Integration by parts will be used repeatedly. What is the…

A:

Q: 3x5 3x4+6x33x² - 6x Evaluate A B (C) (D) ·S= x²-2x-In x² - 4x 2 x² - 4x 2 x² - 2x 2 + In + In + In…

A:

Q: Question 13 Consider J x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) +…

A:

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

A: We have to find out value

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

A: To find out the bounded area by the curves.

Q: Find S y dy Vy+2 D using the substitution u + 5 = √y+2. A √y+2−5) (5√√y+2+y+24) + C Ⓡ(√9+2-5)…

A:

Q: QUESTION 4 To evaluate use integration by parts. What is the expression after the second integration…

A: We have to solve above integral

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

A:

Q: x dx x² + √√x². The integral - sine de SSH 1 + cose sece tane de sece - 1 sec²0 do 1+tano cose do…

A:

Q: 5ñ Find the area bounded by the trigonometric curves y=sinx and y=cosx from x=to x== 4 (A) 3.667…

A:

Q: 1x3 Inx dx = fx) ((1/4) Inx-B) + C?

A: Integrating by parts.   Hence we get answer 0.

Q: What is the definite integral on the interval [1,3] given by n lim n-∞ €k cos πæk Δα? 3 of x cos x…

A:

Q: 17. Evaluate A. B. C. C 3x4+6x³3x² - 6x x² - 4x 2 x²-2x 2 x² - 4x + In 2 x²-2x-In + In -dx, using…

A: We have to calculate the given indefinite integral according to the given information

Q: ·S- y dy y+2 A (√3+2-5) (5√3+2-y+24)+C ℗(√9+2-8)(5√3+2+7+21)+C Ⓒ(√3+2-5) (5√3+2+y+24)+C…

A:

Q: 3x5 ·S= 3x4+6x³-3x² - 6x x²-2x-In -1 [ + €². (x-1) 1/6(x+2) 16/3 (x+1) 1/2 +C x² - 4x (x − 1)…

A: