If the definite integral I=∫0πsin⁡xdx=∑ε=0na_(ε)sin⁡ε. (where, ⋅ is the greatest integer function), then the value of (a_n+n)/(π) is equal to

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MARKS Content Team · Accepted Answer

Correct answer: 1. The given integral is I=∫01sin⁡0dx+∫12sin⁡1dx+∫23sin⁡2dx+∫3πsin⁡3dx ⇒I=2-1sin⁡1+3-2sin⁡2+π-3sin⁡3 ∴a_n=π-3 and n=3 ⇒a_n+n=π or (a_n+n)/(π)=1

If the definite integral $I = \int_{0}^{π} \sin [x] d x = \sum_{ε = 0}^{n} a_{ε} \sin ε .$ (where, $[\cdot]$ is the greatest integer function), then the value of $\frac{a_{n} + n}{π}$ is equal to

Solution

More Definite Integration Questions

If the definite integral I=∫0πsin⁡xdx=∑ε=0naεsin⁡ε. (where, ⋅ is the greatest integer function), then the value of an+nπ is equal to

Solution

More Definite Integration Questions

If the definite integral $I = \int_{0}^{π} \sin [x] d x = \sum_{ε = 0}^{n} a_{ε} \sin ε .$ (where, $[\cdot]$ is the greatest integer function), then the value of $\frac{a_{n} + n}{π}$ is equal to