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What is the integration of 24sin cube of x times 2sin of x times cos of x dx upper limit of 0 to 75 degrees?
Wiki User
∙ 11y ago
It looks like you want to integrate { [24*sin³(x)]*[2*sin(x)]*[cos(x)]dx }. Note that sin³(x) is the same as [sin(x)]³, so this can simplify to 48*[sin(x)]4*cos(x)*dx.
Let u = sin(x), then du = cos(x)dx, so we have 48*u4*du, which integerates to 9.6*u5 + C. So we have 9.6*[sin(75°)]5 - 9.6*[sin(0°)]5 = 9.6*[sin(75°)]5 - 0 = 8.072166728
Note: When taking derivatives and integrals of trigonometric functions, it only works when using radians (so 75° is 5*pi/12 radians).
I verified my calculations by integrating numerically from 0 to 1.309 radians in 0.01 increments on a spreadsheet {the last 0.009 in 0.001 increments} (using the Trapezoidal method), and got 8.07197 which is less than 0.003% difference from the number calculated by Calculus & Trig.
Wiki User
∙ 11y ago
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