Solve these indefinite and definite integrals.
[integration sign] 4j-5j^3 dj
I got 2j^2 - 5/4j^4... is this my final answer?
If j is the variable, for the indefinite integral you have to add a constant. For the definite integral, you have to put in the lower, upper limits.
j is an unusual variable symbol, I am use to j being sqrt -1
To solve the given indefinite integral of 4j - 5j^3 with respect to j, you need to apply the power rule of integration. The power rule states that the integral of x^n with respect to x is (x^(n+1))/(n+1) + C, where C is the constant of integration.
So, let's apply the power rule to each term of the given integral:
∫(4j - 5j^3) dj
= (4/2)j^2 - (5/4)(j^3+1)/(3+1) + C
= 2j^2 - (5/4)(1/4)j^4 + C
Therefore, your answer for the indefinite integral is 2j^2 - (5/16)j^4 + C, where C is the constant of integration.
Now, if you had a definite integral, you would need to evaluate the integral between specific limits. For example, if you were asked to find the definite integral of 4j - 5j^3 from a to b, you would write:
∫[a to b] (4j - 5j^3) dj
To evaluate this definite integral, you would plug in the upper limit (b) and subtract the value obtained by plugging in the lower limit (a).