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Use method of substitution to integrate the function f(x) = (4x + 5)6 and the answer is
- a)1/28 (4x + 5)7 + k
- b)(4x + 5)7/7 + k
- c)(4x + 5)7/7
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Use method of substitution to integrate the function f(x) = (4x + 5)6 ...
To integrate the given function f(x) = (4x - 5)^6, we can use the method of substitution.
Let u = 4x - 5, then du/dx = 4 and dx = du/4.
Substituting these values into the integral, we get:
∫(4x - 5)^6 dx = ∫u^6 (du/4)
= (1/4) ∫u^6 du
= (1/4) [(1/7)u^7 + C]
= (1/28)(4x - 5)^7 + C
Therefore, the correct answer is option A, (4x - 5)^7/28.
Let u = 4x - 5, then du/dx = 4 and dx = du/4.
Substituting these values into the integral, we get:
∫(4x - 5)^6 dx = ∫u^6 (du/4)
= (1/4) ∫u^6 du
= (1/4) [(1/7)u^7 + C]
= (1/28)(4x - 5)^7 + C
Therefore, the correct answer is option A, (4x - 5)^7/28.
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Community Answer
Use method of substitution to integrate the function f(x) = (4x + 5)6 ...
Given
f(x)=(4x+5)6
Put t=4x+5
dt=4
dx
1dt=dx
4
NOW,,,,,
= 1 $ t6
4
=. 1 t7 +K
4
= 1 [4x+5]7+k
28. , which is your required answer..
f(x)=(4x+5)6
Put t=4x+5
dt=4
dx
1dt=dx
4
NOW,,,,,
= 1 $ t6
4
=. 1 t7 +K
4
= 1 [4x+5]7+k
28. , which is your required answer..
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Use method of substitution to integrate the function f(x) = (4x + 5)6 and the answer isa)1/28 (4x + 5)7 + kb)(4x + 5)7/7 + kc)(4x + 5)7/7d)none of theseCorrect answer is option 'A'. Can you explain this answer?
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