correctly formatted mathematical expression (ie. expressions involving roots, Eu

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correctly formatted mathematical expression (ie. expressions involving roots, Euler's number, greek symbols, trig functions, etc.). No variables (letters and symbols) are case sensitive. The message, "Your answer cannot be understood or graded" will appear when a (ie. missing operands, incorrect grouping operators, misspelled units symbols with no meaning in response has been madeou w submissions for syntax errors. Please see the topic, Answering Math and Science Questions, under the WebAssign Student Help Sy detailed information and examples 7. 1 points SCalc7 16.2.004 Evaluate the line integral, where C is the given curve. x sin(y) ds, C is the line segment from (0, 4) to (3, 8) Need Help? Read It Talk to a Tutor Submit Answer Save Progress

Explanation / Answer

(0,4) to (3,8)

x(t) =0+ (3-0)t , y(t)=4+ (8-4) t , 0t1

x(t) =3t , y(t)=4+ 4t , 0t1

x'(t) =3 , y'(t)=4

ds=[(x'(t))2+(y'(t))2] dt

ds=[32+42] dt

ds=5 dt

c x sin(y) ds =[0 to 1] 3t sin(4+4t) 5 dt

c x sin(y) ds =[0 to 1] 15t sin(4+4t) dt

integration by parts :u =15t , dv= sin(4+4t) dt , du =15 dt , v= -(1/4)cos(4+4t) , u dv =uv -v du

c x sin(y) ds =|[0 to 1] 15t(-(1/4)cos(4+4t)) -[0 to 1] (-(1/4)cos(4+4t)) 15 dt

c x sin(y) ds =|[0 to 1] (-(15t/4)cos(4+4t)) -|[0 to 1] (-(15/16)sin(4+4t))

c x sin(y) ds =|[0 to 1] (-(15t/4)cos(4+4t)) +|[0 to 1] ((15/16)sin(4+4t))

c x sin(y) ds =(-(15/4)cos(4+4)) -(-(15*0/4)cos(4+0))  +((15/16)sin(4+4)) -((15/16)sin(4+0))

c x sin(y) ds =(-(15/4)cos(8)) -0 +((15/16)sin(8)) -((15/16)sin(4))

c x sin(y) ds =(15/16)(-4cos(8) +sin(8) -sin(4)) 2.1827

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