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KCET2023MathematicsDefinite Integration

₂^8 5^ 10-x 5^ x +5^ 10-x d x is equals to

Options

  1. A6
  2. B4
  3. C3
  4. D5

Correct answer

C. 3

Step-by-step solution

Let I= ₂^8 5^ 10-x 5^ x +5^ 10-x d x Using property ₀^a f(x) d x= ₀^a f(0+a-x) d x aligned & I= ₂^8 5^ 10-(2+8-x) & I= ₂^8 5^ 10-10+x 5^ 10-x +5^ 10-10+x & I= ₂^8 5^ x 5^ 10-x +5^ x aligned Adding Eqs. (i) and (ii), we get aligned & 2 I= ₂^8 5^ 10-x +5^ x 5^ x +5^ 10-x d x & I I= ₂^8 d x & I= 1 2 [x]₂^8= 1 2 6=3 aligned

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