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Andreas93 [3]
3 years ago
12

Evaluate the integral. (Assume a ≠ b. Remember to use absolute values where appropriate. Use C for the constant of integration.)

5 (x + a)(x + b) dx
Mathematics
1 answer:
Bess [88]3 years ago
4 0

Answer:

<u><em>F(x)= 5*[\frac{x^{3} }{3} + (a*b)*\frac{x^{2} }{2} + a*b*x + C.</em></u>

Step-by-step explanation:

<u><em>First step we aplicate distributive property to the function.</em></u>

<u><em>5*(x+a)*(x+b)= 5*[x^{2}+x*b+a*x+a*b]</em></u>

<u><em>5*[x^{2}+x*(b+a)+a*b]= f(x), where a, b are constant and a≠b</em></u>

<u><em>integrating we find ⇒∫f(x)*dx= F(x) + C, where C= integration´s constant</em></u>

<u><em>∫^5*[x^{2}+x*(a+b)+a*b]*dx, apply integral´s property</em></u>

<u><em>5*[∫x^{2}dx+∫(a*b)*x*dx + ∫a*b*dx], resolving the integrals </em></u>

<u><em>5*[\frac{x^{3} }{3} + (a*b)*\frac{x^{2} }{2} + a*b*x</em></u>

<u><em>Finally we can write the function F(x)</em></u>

<u><em>F(x)= 5*[\frac{x^{3} }{3} + (a*b)*\frac{x^{2} }{2} + a*b*x ]+ C.</em></u>

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