0-100pi-sinx-dx-

Question Number 117006 by TANMAY PANACEA last updated on 08/Oct/20

\int_{0}^{100 π} ∣ s i n x ∣ d x

Commented by TANMAY PANACEA last updated on 08/Oct/20

t h a n k y o u s i r

Answered by mathmax by abdo last updated on 08/Oct/20

let I = \int_{0}^{100 π} ∣ sinx ∣ dx \Rightarrow I = \sum_{k = 0}^{99} \int_{k π}^{(k + 1) π} ∣ sinx ∣ dx

=_{x = k π + u} \sum_{k = 0}^{99} \int_{0}^{π} ∣ {(- 1)}^{k} sinu ∣ du = \sum_{k = 0}^{99} \int_{0}^{π} sinu du

= \sum_{k = 0}^{99} {[- cosu]}_{0}^{π} = 2 \sum_{k = 0}^{99} (1) = 2 \times 100 = 200

Commented by TANMAY PANACEA last updated on 08/Oct/20

t h a n k y o u s i r

Commented by Bird last updated on 09/Oct/20

y o u a r e w e l c o m e s i r

Answered by TANMAY PANACEA last updated on 08/Oct/20

∣ s i n x ∣ g r a p h i s a l a w a y s + v e a n d e a c h l o o p o f

s i n x a r e a i s 2 . h e r e 100 l o o p s o a r e a i s 2 \times 100 = 200

\int_{0}^{100 π} ∣ s i n x ∣ d x = 100 \int_{0}^{π} ∣ s i n x ∣ d x = 100 ∣ - c o s x ∣_{0}^{π}

= - 100 (- 1 - 1) = 200