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Integral cos 3 (2x) dx ▼Math Symbols ▲Math Symbols

Common forms and functions
  • x+y x+y
  • x·yx*y
  • x/yx÷y
  • xyx**y
  • √xsqrt(x)
  • x!factorial(x)
  • ln(x)log(x)
  • exexp(x)
  • log10(x)log(x, 10)
  • log2(x)log(x, 2)
  • sin(x)sin(x)
  • cos(x)cos(x)
  • tan(x)tan(x)
  • cot(x)1/tan(x)
  • atan(x)atan(x)
  • asin(x)asin(x)
  • acos(x)acos(x)
  • sinh(x)sinh(x)
  • cosh(x)cosh(x)
  • tanh(x)tanh(x)
  • eE
  • πpi
  • Compute \int \cos^{3}(2x)dx

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Integral sin4 (x) cos2 (x) d ▼Math Symbols ▲Math Symbols

Common forms and functions
  • x+y x+y
  • x·yx*y
  • x/yx÷y
  • xyx**y
  • √xsqrt(x)
  • x!factorial(x)
  • ln(x)log(x)
  • exexp(x)
  • log10(x)log(x, 10)
  • log2(x)log(x, 2)
  • sin(x)sin(x)
  • cos(x)cos(x)
  • tan(x)tan(x)
  • cot(x)1/tan(x)
  • atan(x)atan(x)
  • asin(x)asin(x)
  • acos(x)acos(x)
  • sinh(x)sinh(x)
  • cosh(x)cosh(x)
  • tanh(x)tanh(x)
  • eE
  • πpi
  • Compute \int sin^{4}(x)cos^{2}(x)dx

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An Alternate Solution ▼Hint ▲Hint ▼Math Symbols ▲Math Symbols

pay particular attention to your limits of integration.
Common forms and functions
  • x+y x+y
  • x·yx*y
  • x/yx÷y
  • xyx**y
  • √xsqrt(x)
  • x!factorial(x)
  • ln(x)log(x)
  • exexp(x)
  • log10(x)log(x, 10)
  • log2(x)log(x, 2)
  • sin(x)sin(x)
  • cos(x)cos(x)
  • tan(x)tan(x)
  • cot(x)1/tan(x)
  • atan(x)atan(x)
  • asin(x)asin(x)
  • acos(x)acos(x)
  • sinh(x)sinh(x)
  • cosh(x)cosh(x)
  • tanh(x)tanh(x)
  • eE
  • πpi


  • As Professor Miller explained in lecture, the area of the region show in Figure1  is \int_{0}^{b}\sqrt{a^{2}-x^{2}} dx Use the substitution x = a cos 0 to solve this 0 integral.

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Massachusetts Institute Of Technology
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Instructor: David Jerison

View the complete course at: http://ocw.mit.edu/18-01F06

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