Assignment#2 – Math160 STUDENT NAME ——————————————- Student I.D ——————————— Due April 12, 2017. FULL HANDWRITTEN NEAT AND CLEAR SOLUTIONS REQUIRED. Assignment should be handed in as a hard copy in class. You can use the notes and textbook, but if you are caught copying from another student ( and you will) both students will receive a mark of zero and Incident of cheating report will be filed and submitted to a Chair with all the repercussions. Don’t take any risks. I reserve the right to ask any student to show any question from the assignment on the board in class after submission of the assignment. Find the area under the curvef(x)=2x-x^2, between x=0 and x=3 by :using Riemann Sum. /5 Find y as a function of x, given that dy/dx=8x+1 and the curve passes through the point (-1,4). /5 A person skis down a slope with an acceleration (in m/s^2) given by a= 600t/(60+0.5t^2 )^2 , where t is the time (in s). Find the skier’s velocity as a function of time if v=0 when t=0. /5 Evaluate the following integrations: a). ∫_3^7▒〖√(16t^2+8t+1) dt〗 /3 b). ∫_0^1▒〖(y+1)^5 dy〗 /4 c). /3 Integrate. Write your answers in simplified, fully factored form without negative exponents for full marks. (Show all your work for potential partial marks). ∫▒〖tan〗^3x dx ∫▒(〖cot〗^2x-sinx)/〖cos〗^2x dx ∫▒(1-sinx)/(1+cosx ) dx /4 d). ∫▒〖x^3 ln(2x)〗 dx e).∫▒〖x cos〖(2x)〗 〗 f). ∫▒〖e^x sinx 〗 dx /5 g). ∫▒6/√(9+x^2 ) dx Use partial fractions to integrate. (Show all your work for potential partial marks). a). ∫▒〖 (x-16)/(〖 x〗^2-5x-14 )〗 dx b). ∫▒〖 x/(〖x(x^2+1)〗^2 (x-3)^2 )〗 dx Integrate the following by using the “Table of Integrals”, indicate the no. and the constants. (3) a) (3) b) (3) c)

Assignment#2 – Math160 STUDENT NAME ——————————————- Student I.D ——————————— Due April 12, 2017. FULL HANDWRITTEN NEAT AND CLEAR SOLUTIONS REQUIRED. Assignment should be handed in as a hard copy in class. You can use the notes and textbook, but if you are caught copying from another student ( and you will) both students will receive a mark of zero and Incident of cheating report will be filed and submitted to a Chair with all the repercussions. Don’t take any risks. I reserve the right to ask any student to show any question from the assignment on the board in class after submission of the assignment. Find the area under the curvef(x)=2x-x^2, between x=0 and x=3 by :using Riemann Sum. /5 Find y as a function of x, given that dy/dx=8x+1 and the curve passes through the point (-1,4). /5 A person skis down a slope with an acceleration (in m/s^2) given by a= 600t/(60+0.5t^2 )^2 , where t is the time (in s). Find the skier’s velocity as a function of time if v=0 when t=0. /5 Evaluate the following integrations: a). ∫_3^7▒〖√(16t^2+8t+1) dt〗 /3 b). ∫_0^1▒〖(y+1)^5 dy〗 /4 c). /3 Integrate. Write your answers in simplified, fully factored form without negative exponents for full marks. (Show all your work for potential partial marks). ∫▒〖tan〗^3x dx ∫▒(〖cot〗^2x-sinx)/〖cos〗^2x dx ∫▒(1-sinx)/(1+cosx ) dx /4 d). ∫▒〖x^3 ln(2x)〗 dx e).∫▒〖x cos〖(2x)〗 〗 f). ∫▒〖e^x sinx 〗 dx /5 g). ∫▒6/√(9+x^2 ) dx Use partial fractions to integrate. (Show all your work for potential partial marks). a). ∫▒〖 (x-16)/(〖 x〗^2-5x-14 )〗 dx b). ∫▒〖 x/(〖x(x^2+1)〗^2 (x-3)^2 )〗 dx Integrate the following by using the “Table of Integrals”, indicate the no. and the constants. (3) a) (3) b) (3) c)

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