Integrate: (x² + 2x + 3) with respect to x within limit (x = 0) to (x = 1)
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Integrate: (x² + 2x + 3) with respect to x within limit (x = 0) to (x = 1)
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To integrate the function f(x) = x² + 2x + 3 with respect to x over the given limits [0, 1], you can use the definite integral formula. Here's how you can do it:
∫[0 to 1] (x² + 2x + 3) dx
Now, integrate term by term:
∫[0 to 1] x² dx + ∫[0 to 1] 2x dx + ∫[0 to 1] 3 dx
Integrate each term separately:
(1/3)x³ + (x²) + (3x) | from 0 to 1
Now, plug in the upper and lower limits:
[(1/3)(1)³ + (1)² + (3(1))] - [(1/3)(0)³ + (0)² + (3(0))]
Simplify:
(1/3 + 1 + 3) - (0 + 0 + 0)
(1/3 + 1 + 3)
Now, add the values:
1/3 + 1 + 3 = 10/3
So, the integral of (x² + 2x + 3) with respect to x from 0 to 1 is 10/3.
Hope it's helpful
Mark as brainlest