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Use of Eulers Theorem

Integrals class 12 of Class 12

Use of Euler’s Theorem

eiθ = cos θ + i sin θ in evaluating integrals

(a) Use of Euler’s Theoremcos bx dx and

(b) Use of Euler’s Theoremsin bx dx

Let P = Use of Euler’s Theoremcos bx dx and Q = Use of Euler’s Theoremsin bx dx

Then P + iQ = Use of Euler’s Theorem = Use of Euler’s Theorem

Equating real and imaginary parts on both sides

P = Use of Euler’s Theorem Or Use of Euler’s Theorem

Where r = Use of Euler’s Theorem and ϕ = tan-1b/a

Likewise Q = Use of Euler’s Theorem

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