Integrate 4 x³+3 x²-2 x+5

Correct Answer is : x4+x3−x2+5x+kx^{4}+x³-x²+5 x+kx4+x3−x2+5x+k

Correct Answer is : x4+x3−x2+5x+kx^{4}+x³-x²+5 x+kx4+x3−x2+5x+k

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Integral Calculus

Question : 46 of 73

Marks: +1, -0

Integrate

4 x^{3}+3 x^{2}-2 x+5

Solution:

Concept:

Integrate term by term using the power rule of integration.

Explanation:

Apply the formula

\int x^n\,dx = \frac{x^{n+1}}{n+1} + k

to each term.

\int 4x^3\,dx = 4 \cdot \frac{x^{4}}{4} = x^4

\int 3x^2\,dx = 3 \cdot \frac{x^{3}}{3} = x^3

\int (-2x)\,dx = -2 \cdot \frac{x^{2}}{2} = -x^2

\int 5\,dx = 5x

Add an arbitrary constant

k

Thus the integral is

x^4 + x^3 - x^2 + 5x + k

Answer:

x^4 + x^3 - x^2 + 5x + k

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