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The area bounded by the curve y = x3, x-axis and two ordinates x = 1 to x = 2 is equal to
- a)15/2 sq. unit
- b)15/4 sq. unit
- c)17/2 sq. unit
- d)17/4 sq. unit
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The area bounded by the curve y = x3, x-axis and two ordinates x = 1 t...
Explanation:
To find the area bounded by the curve y = x^3, x-axis, and the ordinates x = 1 and x = 2, we can use definite integration.
Step 1: Graphing the Curve
First, let's graph the curve y = x^3. The graph of this curve is a cubic function that passes through the origin (0,0) and has a positive slope.
Step 2: Finding the Points of Intersection
Next, we need to find the points of intersection between the curve and the x-axis. To do this, we set y = 0 and solve for x:
0 = x^3
x = 0
So, the curve intersects the x-axis at the origin (0,0).
Step 3: Setting up the Definite Integral
To find the area bounded by the curve, x-axis, and the ordinates x = 1 and x = 2, we need to set up the definite integral. The area can be found by integrating the curve between these two x-values:
A = ∫(from 1 to 2) x^3 dx
Step 4: Evaluating the Definite Integral
Now, we can evaluate the definite integral to find the area:
A = [x^4/4] (from 1 to 2)
A = [(2^4/4) - (1^4/4)]
A = (16/4) - (1/4)
A = 15/4
So, the area bounded by the curve y = x^3, x-axis, and the ordinates x = 1 and x = 2 is equal to 15/4 square units.
Final Answer: Option B (15/4 square units)
To find the area bounded by the curve y = x^3, x-axis, and the ordinates x = 1 and x = 2, we can use definite integration.
Step 1: Graphing the Curve
First, let's graph the curve y = x^3. The graph of this curve is a cubic function that passes through the origin (0,0) and has a positive slope.
Step 2: Finding the Points of Intersection
Next, we need to find the points of intersection between the curve and the x-axis. To do this, we set y = 0 and solve for x:
0 = x^3
x = 0
So, the curve intersects the x-axis at the origin (0,0).
Step 3: Setting up the Definite Integral
To find the area bounded by the curve, x-axis, and the ordinates x = 1 and x = 2, we need to set up the definite integral. The area can be found by integrating the curve between these two x-values:
A = ∫(from 1 to 2) x^3 dx
Step 4: Evaluating the Definite Integral
Now, we can evaluate the definite integral to find the area:
A = [x^4/4] (from 1 to 2)
A = [(2^4/4) - (1^4/4)]
A = (16/4) - (1/4)
A = 15/4
So, the area bounded by the curve y = x^3, x-axis, and the ordinates x = 1 and x = 2 is equal to 15/4 square units.
Final Answer: Option B (15/4 square units)
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Community Answer
The area bounded by the curve y = x3, x-axis and two ordinates x = 1 t...
Area bounded = integration of x^3 ( limit x= 1 to x= 2)
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The area bounded by the curve y = x3, x-axis and two ordinates x = 1 to x = 2 is equal toa)15/2 sq. unitb)15/4 sq. unitc)17/2 sq. unitd)17/4 sq. unitCorrect answer is option 'B'. Can you explain this answer?
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