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Math Help - Integration guidance please

  1. #1
    Newbie
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    Integration guidance please

    hello

    would just like some help checking my work:

    Q:
    Estimate area under curve if y= 1/1+cosx between x=0 and pi/2 with 3 ordinates.

    A: 2 strips therefore h = (pi/2) - 0 /2 = 0.785 3dp

    x = 0,pi/4, pi/2
    y=0.5, 0.500, 0.500

    trapezium rule : h/2 (y0 +y2 +2(y1)----> 0.785/2 (0.5+0.500+0.500+2(0.500)
    = 0.785...is this correct because answer says 1.049 or am i correct and answer wrong, please can you show me where i have gone wrong.


    Q:
    determine the following indefinite integrals:
    y=(integration sign) 3/4 e^2x dx
    -----> i got (3/4)/2 e^2x +c---->please can you show me where i have gone wrong if so.
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  2. #2
    MHF Contributor
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    f(x) = \dfrac{1}{1+\cos{x}}

    \displaystyle \int_0^{\frac{\pi}{2}} f(x) \, dx \approx \frac{\pi}{8}\left[f(0) + 2f\left(\frac{\pi}{4}\right) + f\left(\frac{\pi}{2}\right)\right]
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