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The integral of px3 + qx2 + rk + w/x is equal to
- a)px2 + qx + r + k
- b)px3/3 + qx2/2 + rx
- c)3px + 2q – w/x2
- d)none of these
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The integral of px3 + qx2 + rk + w/x is equal toa)px2 + qx + r + kb)px...
**Explanation:**
In order to find the integral of the given expression, we need to apply the power rule of integration, which states that the integral of x^n with respect to x is equal to (x^(n+1))/(n+1), where n is any real number except -1.
Let's break down the given expression and apply the power rule to each term separately.
1. Integral of px^3 with respect to x:
Using the power rule, we get (px^(3+1))/(3+1) = (px^4)/4.
2. Integral of qx^2 with respect to x:
Using the power rule, we get (qx^(2+1))/(2+1) = (qx^3)/3.
3. Integral of rk with respect to x:
Since rk is a constant, its integral with respect to x is rkx.
4. Integral of w/x with respect to x:
This term can be rewritten as w * (1/x), and since w is also a constant, we can pull it out of the integral:
w * integral of 1/x with respect to x.
The integral of 1/x with respect to x is ln|x|, so the integral becomes w * ln|x|.
Now, let's add up all the integrals we found:
(px^4)/4 + (qx^3)/3 + rkx + w * ln|x|
The given options do not match this result, so none of the options is correct. Therefore, the correct answer is option 'D' (none of these).
It's important to note that in order to find the integral, we need to know the limits of integration or specify that it is an indefinite integral. Without the limits or specifying it as indefinite, we cannot provide a specific numerical result for the integral.
In order to find the integral of the given expression, we need to apply the power rule of integration, which states that the integral of x^n with respect to x is equal to (x^(n+1))/(n+1), where n is any real number except -1.
Let's break down the given expression and apply the power rule to each term separately.
1. Integral of px^3 with respect to x:
Using the power rule, we get (px^(3+1))/(3+1) = (px^4)/4.
2. Integral of qx^2 with respect to x:
Using the power rule, we get (qx^(2+1))/(2+1) = (qx^3)/3.
3. Integral of rk with respect to x:
Since rk is a constant, its integral with respect to x is rkx.
4. Integral of w/x with respect to x:
This term can be rewritten as w * (1/x), and since w is also a constant, we can pull it out of the integral:
w * integral of 1/x with respect to x.
The integral of 1/x with respect to x is ln|x|, so the integral becomes w * ln|x|.
Now, let's add up all the integrals we found:
(px^4)/4 + (qx^3)/3 + rkx + w * ln|x|
The given options do not match this result, so none of the options is correct. Therefore, the correct answer is option 'D' (none of these).
It's important to note that in order to find the integral, we need to know the limits of integration or specify that it is an indefinite integral. Without the limits or specifying it as indefinite, we cannot provide a specific numerical result for the integral.
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The integral of px3 + qx2 + rk + w/x is equal toa)px2 + qx + r + kb)px...
Integral of x^n = x^n+1/n+1
Based on the above formula,
Integral of px³ = px⁴/4 which is not the term of any of the option.
Even with the integration of first term , we can say that none will be answer. So correct answer is option D
Based on the above formula,
Integral of px³ = px⁴/4 which is not the term of any of the option.
Even with the integration of first term , we can say that none will be answer. So correct answer is option D
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