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📐 Mathematics  ·  Integrals  ·  JEE

Integrate using substitution: integral of 2x(x²+1)⁵ dx

Answer: (x²+1)⁶/6 + C.

  • A (x²+1)⁶/6 + C
  • B (x²+1)⁶ + C
  • C 10x(x²+1)⁴ + C
  • D 2x(x²+1)⁶/6 + C

Correct answer: A. (x²+1)⁶/6 + C

Explanation: Let u = x²+1, du = 2x dx. Integral = u⁵ du = u⁶/6 = (x²+1)⁶/6 + C.

xyabArea = integral of f(x) dxRectangles approximate the area (Riemann sum)

The exact area under the curve from a to b (shaded) is approximated by a few rectangles, the Riemann sum idea behind the definite integral.

Concept context

Indefinite and definite integrals, areas under curves

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