Question

integrate the function √x with respect to X and find within the limits x=2 to 4​

Answer 1

Answer:

READ THE MENTIONED IMAGE OR

:-

∫⁴ √x dx = ∫⁴ (x^½) dx

² ²

= x^(½ + 1) ˥⁴

(½ + 1) │ by the Power Rule for Integration and by the

˩² Fundamental Theorem of Calculus for definite

integration

= x^(3/2) ˥⁴

(3/2) │

˩²

= (2/3)x^(3/2)˥⁴

˩²

= (2/3)4^(3/2) ― (2/3)2^(3/2) by the Fundamental

Theorem of Calculus

for definite integration

= (2/3)[4^(3/2) ― 2^(3/2)]

= (2/3)(√4³ ― √2³)

= (2/3)(√64 ― √8 )

= (2/3){8 ― √[4(2)]}

= (2/3)(8 ― √4√2)

= (2/3)(8 ― 2√2)

= (2/3)(2)(4 ― √2)

= (4/3)(4 ― √2) or

= 3.44772 (rounded to 5 decimal places)

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Answer 2

2|4x−−√dx=[23xx−−√]42

=4(4−2–√)3