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What is the area under the curve f (x) = xex above the Xaxis and between the lines x = 0 and x = 1?
- a)1/2 sq. unit
- b)1 sq. unit
- c)3/2 sq. units
- d)2 sq. units
Correct answer is option 'A'. Can you explain this answer?
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What is the area under the curve f (x) = xex above the Xaxis and betwe...
Area under the curve f(x) = xex
The area under the curve of a function between two points can be found by evaluating the definite integral of the function over that interval. In this case, we are interested in finding the area under the curve of the function f(x) = xex between x = 0 and x = 1.
Calculating the area
To find the area under the curve f(x) = xex between x = 0 and x = 1, we need to evaluate the definite integral of the function over this interval. The definite integral of xex can be found using integration techniques.
Integrating xex with respect to x, we get:
∫xex dx = xex - ex + C
Now, we can evaluate this integral over the interval [0, 1] to find the area under the curve.
Substitute x = 1:
1e1 - e1 - (0e0 - e0) = e - e = 0
Substitute x = 0:
0e0 - e0 = -1
Therefore, the area under the curve f(x) = xex above the x-axis and between the lines x = 0 and x = 1 is 1/2 square units.
This calculation shows that the area under the curve of the function xex between x = 0 and x = 1 is 1/2 square units.
The area under the curve of a function between two points can be found by evaluating the definite integral of the function over that interval. In this case, we are interested in finding the area under the curve of the function f(x) = xex between x = 0 and x = 1.
Calculating the area
To find the area under the curve f(x) = xex between x = 0 and x = 1, we need to evaluate the definite integral of the function over this interval. The definite integral of xex can be found using integration techniques.
Integrating xex with respect to x, we get:
∫xex dx = xex - ex + C
Now, we can evaluate this integral over the interval [0, 1] to find the area under the curve.
Substitute x = 1:
1e1 - e1 - (0e0 - e0) = e - e = 0
Substitute x = 0:
0e0 - e0 = -1
Therefore, the area under the curve f(x) = xex above the x-axis and between the lines x = 0 and x = 1 is 1/2 square units.
This calculation shows that the area under the curve of the function xex between x = 0 and x = 1 is 1/2 square units.
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What is the area under the curve f (x) = xex above the Xaxis and between the lines x = 0 and x = 1?a)1/2 sq. unitb)1 sq. unitc)3/2 sq. unitsd)2 sq. unitsCorrect answer is option 'A'. Can you explain this answer?
Question Description
What is the area under the curve f (x) = xex above the Xaxis and between the lines x = 0 and x = 1?a)1/2 sq. unitb)1 sq. unitc)3/2 sq. unitsd)2 sq. unitsCorrect answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about What is the area under the curve f (x) = xex above the Xaxis and between the lines x = 0 and x = 1?a)1/2 sq. unitb)1 sq. unitc)3/2 sq. unitsd)2 sq. unitsCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the area under the curve f (x) = xex above the Xaxis and between the lines x = 0 and x = 1?a)1/2 sq. unitb)1 sq. unitc)3/2 sq. unitsd)2 sq. unitsCorrect answer is option 'A'. Can you explain this answer?.
What is the area under the curve f (x) = xex above the Xaxis and between the lines x = 0 and x = 1?a)1/2 sq. unitb)1 sq. unitc)3/2 sq. unitsd)2 sq. unitsCorrect answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about What is the area under the curve f (x) = xex above the Xaxis and between the lines x = 0 and x = 1?a)1/2 sq. unitb)1 sq. unitc)3/2 sq. unitsd)2 sq. unitsCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the area under the curve f (x) = xex above the Xaxis and between the lines x = 0 and x = 1?a)1/2 sq. unitb)1 sq. unitc)3/2 sq. unitsd)2 sq. unitsCorrect answer is option 'A'. Can you explain this answer?.
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