Solve the integral. \int_{1}^{9}t^{-\frac{1}{2}}dt

grislingatb

grislingatb

Answered question

2021-11-23

Solve the integral.
19t12dt

Answer & Explanation

Drood1980

Drood1980

Beginner2021-11-24Added 16 answers

Step 1
To find:
The definite integral of 19t12dt.
Formula used:
Power rule of integration:
(xn)=nxn1
Calculation:
The definite integral of 19t12dt can be obtained as,
19t12dt=[t12+112+1]19
=2[t]19
=2[91]
=4
Step 2
Thus, the integral of 19t12dt is 4.
Kathleen Ashton

Kathleen Ashton

Beginner2021-11-25Added 15 answers

Step 1: Use Negative Power Rule: xa=1xa.
191tdt
Step 2: If f(x) is a continuous function from a to b, and if F(x) is its integral, then:
abf(x)dx=F(x)ab=F(b)F(a)
Step 3: In this case, f(t)=1t. Find its integral.
2t19
Step 4: Since F(t)ab=F(b)F(a), expand the above into F(9)−F(1):
2921
Step 5: Simplify.
4

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