y = t3 +1 x = Int d50y olduğuna göre dx50 X = O D) 349 Da) 349t2 TO) 349t OB) 349t3 O NS) 350t3

Q: Find both first partlal deriva N = sinh(8x + 13y)

A: The function given is z= sinh(8x+13y) and we know that derivative of sinhx is coshx

Q: (a) Use the trapezoidal rule to approximate the integral. dx

A: Solution of given question is written in below steps.

Q: by using the double integration, find the area that lies inside the curve r= (8cos e) and outside…

A: Given: The curves r=8cosθ    and r=4

Q: Evaluate the trigonomnetric integral ∫(sint)5(cost)3dt

A: Given, ∫sint5cost3dt  We have to evaluate the  integral

Q: Estimate the area between the function y = 2x2 + 2x +1 and the a-axis on the interval [4, 7] using 3…

A: GIVEN DATA :  Function y=2x2+2x+1 on the x-axis in the interval 4,7       TO FIND : Area by using…

Q: 81x² Vy? + 16 dy dx ,2 3x

A:

Q: Evaluate the integral by reversing the order of integration. 16 dy dx y³ + 1

A: From the given problem, it is observed that the region of integration is x,y: x≤y≤4; 0≤x≤16. Draw…

Q: What is the volume of a solid object formed by rotating the region between f (x) =6x² + 3 and g (x)…

A: Let the region bounded by the curves fx=6x2+3 and gx=4x2-3 be R.  R is rotated about the line y=-3…

Q: Calculate the integral by interchanging the order of integration. (x + 3eY – 4) dx) dy Jo

A:

Q: Calculate the ollowing inte fCx)-ユ) tny the fx)dx=D- 9)CI f(x) dx= 4

A:

Q: Use double integral to find the average temperature of T(x. y) = 10-8r -2y

A: Temperature function is given as - Tx, y = 10-8x2-2y2Average temperature = ∬10-8x2-2y2dxdyGiven…

Q: (c) 5tª Int dt

A:

Q: use the integration by parts to evaluate the intergral  x In2 x.dx

A:

Q: Evaluate thl integraus in H3) dx (44) dx dx 17 +x? 45

A: Disclaimer:  Since you have posted multiple questions, I will answer first three questions. If you…

Q: Q4A) Find area bounded by y = 0.y = √2x-x² using double integration.

A: We are authorized to answer one question at a time since you have not mentioned which question you…

Q: Use Property 8 to estimate the value of the integral.

A: Given:

Q: Use the 4-segments multiple Trapezoidal rule to estimate the integral L VI+ z*dz

A: Given that  The integral is  To find the integral by using trapezoidal rule

Q: Find the integral ∫y (square root of y+2) dy

A: To find: ∫ yy+2dy

Q: Use Property 8 to estimate the value of the integral.

A:

Q: Set up an integral to represent the total mass of a 2×5 rectangular sheet, whose density per unit…

A:

Q: Evaluate the integral.  integral y 3 sqrt (y 2 +1 )dx

A: We have to evaluate the integral: ∫y3y2+1dy We will use substitution method to solve this integral…

Q: The area under the curve is negative, if z value is also negative. True or False?

A:

Q: sketch, reverse and evaluate the integral dy dz 15

A:

Q: What is the integral of the constant function f(x, y) = 5 over the rectangle [-2, 3] x [2, 4]?

A: Given:            f(x, y) = 5   over rectangle -2, 3×2, 4

Q: dr Find the percentage error by calculating the integral with the Trapezoidal Formula using n = 4…

A: Given that, the integral is ∫28xx2+1dx. It is known that, the formula for the trapezoidal…

Q: Use trapezoidal rule to estimate the the integral. V + Adx n=6 a) 2.75

A: the given integral is ∫14x2+4dx given n=6 therefore  h=b-an=4-16=36=0.5

Q: re of constant

A:

Q: 2 Evaluate the inteyral. dx dy dz taken. throughout the volumeofsphere 23=

A: We have to solve given integral:

Q: Evaluate the integral. (Use C for the constant of integration.) 19z3e? dz

A: Explanation of the answer is as follows

Q: 15. Use the table of integralsto evaleuate, the integral. ex dx

A: We have to evaluate the integral ∫ex1-e2x32dx by using the table of integrals.

Q: I Sketch the area bounded by x² + 2y = 4 and x+y+2=0 and determine: d) area using horizontal strip…

A:

Q: Assume a pink paint spill spreads in a circular pattern whose radius increases at a rate of 2 in/s.…

A:

Q: Use integration by parts to evaluate x In(x)dx.

A: We have to evaluate integration of xln(x) by parts.

Q: Approximate the integral dx using Simpson's Rule and four rectangles.

A: Given,  ∫121xdx

Q: Make a substitution to express the integrand as arational function and then evaluate the integral.…

A: Given: ∫x3x2+13dx

Q: Evaluate the integral by reversing the order of integration. 12 Se dx dy

A: we have given an integral, I=∫08∫y325ex4dxdy we have limits for x arex=y3 and x=2 x3=y and x=2 we…

Q: Evaluate the integrals below: etanx sec² x 3. a) V(1 – (elanx )2 :. dx, b) / cot5x. dy

A: We need to integrate of the following integrals.

Q: sketch, reverse and evaluate the integral dy dx

A:

Q: YA y= f(x)

A:

Q: find the integral of t sint cost dt

A: Integrand, I = t sint cost dtRecall the formula from trigonometry: sin2t = 2 sint costHence, sint…

Q: DSX 2 X sec /x dx 3

A:

Q: r8 2 dx dy

A:

Q: Use integration by parts to find the indefinite inte 6xe-X dx + C

A:

Q: Calculate the integral by interchanging the order of integration. 16, dy ) dx 1

A:

Q: Use double integral to find the average temperature of 1 (x, y) = tion of o ploto 0<rs4 and 0< y3 5…

A: Given,      T(x, y)=12-6x2-4y2,       0≤x≤4 and 0≤y≤5

Q: dt #2. t Vt? – 16

A:

Q: 1 dx is an improper integra 2 3x

A:

Q: Sketch the region in the first quadrant bounded by the curve x+y2=4, and find its area first by…

A: To graph the function, solve the given equation for y. Since the region is in the first quadrant,…

Q: Use integration by parts to evaluate the integral. ∫xe^4x dx

A:

Q: 5. Ssin' x dx.

A: I am attaching image so that you understand each and every step.