Question

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Answer 1

Answer:

Option (A) 32/3

Step-by-step explanation:

₃∫⁸ x/√1+x

Let , 1+x = t ______(1)

d.w.r. to x

dx = dt

And value of t = 4-> 9

∴ ₄∫⁹(t-1 /√t )dt

• = ₄∫⁹{ (t)½ - (t)⁻½}dt

• = [ 2/3(t)³ˡ² - 2{t^½)]₄⁹

• ={2/3(9)³ˡ² - 2 (9)^½} - [{2/3(4)³ˡ² - 2(4)^½]

• = (2/3×27 - 2× 3 )- [{ 16/3 - 4 }]

• =( 18 - 6) - [{ 16/3 -4}]

• =12 - 16/3 +4

• = 16 - 16/3 = 48-16/3

• 32/3Answer