Let A be the area enclosed between f (x)= 2+cosx 1 1 x==27 and x= 37....

 

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Let A be the area enclosed between f (x)= 2+cosx 1 1 x==27 and x= 37. Let B be the area enclosed between g(x)= 2 2-cos x two lines x== and x= . Show that A = B (the two enclosed area are equal). 2 2 Hints: you can either show the areas A and B are the same, or prove that A - B =0. 3 = the x-axis and the two vertical lines * For the next question QZ, use the following definitions: exp(-x) denotes the exponential function e* *The special value I (3/2) is defined as I (3/2) = f e t dt . For your reference, we have: lim,.... (te) lim, _o(te ) = 0. Q7. (write out all necessary steps/details) (i) Find the indefinite integral 2x e* dx. (Hint: consider to use change of variable). (ii) Show that I'(3/2)=xexp(-x) dx (see definition of T(3/2) above). > the x-axis and the 9/4 (iii) Apply numerical integration to calculate the approximate value of 2 xexp(-x) dx . (You may use 3-5 trapezoids for this calculation). Let A be the area enclosed between f (x)= 2+cosx 1 1 x==27 and x= 37. Let B be the area enclosed between g(x)= 2 2-cos x two lines x== and x= . Show that A = B (the two enclosed area are equal). 2 2 Hints: you can either show the areas A and B are the same, or prove that A - B =0. 3 = the x-axis and the two vertical lines * For the next question QZ, use the following definitions: exp(-x) denotes the exponential function e* *The special value I (3/2) is defined as I (3/2) = f e t dt . For your reference, we have: lim,.... (te) lim, _o(te ) = 0. Q7. (write out all necessary steps/details) (i) Find the indefinite integral 2x e* dx. (Hint: consider to use change of variable). (ii) Show that I'(3/2)=xexp(-x) dx (see definition of T(3/2) above). > the x-axis and the 9/4 (iii) Apply numerical integration to calculate the approximate value of 2 xexp(-x) dx . (You may use 3-5 trapezoids for this calculation).