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00:00 - 00:59 | hello everyone location is find the area bounded by the curve x square equal to 4 Y and the straight line x is equal to 4 Y - 2 so this is the diagram for the question ok so this is a straight line x - 2 and left the curve experiment 4 why so this is the area we have to find out the area for ok so here are the cup latest x square equal to 4 Y and V are the line all that is X is equal to 4 Y - 2 ok so if we find out intersection of these curve and the line so the intersection off the cuff and the line |

01:00 - 01:59 | Agar chart two values that is X is equal to -1 and the second hand at x is equal to 2 ok from the figure the area of the origin that is required to us film equal to the area under the line OK - the area under the curve ok show the area under the line will be integration of -1 to 2 why d x minus area under the curve will be - 122 why DX ok so this will be wife on the line and this will be for the curve now as we have the curve |

02:00 - 02:59 | as x square is equal to 4 Y from here value of minus x square by 4 and similarly we have the line as x is equal to 4 Y - 2 from here we have the value of Y as X + 2 by 4 these two values and equation we have the area as area is equal to integration of -1 to 2 X + 2 by 4 DX - integration of -122 x square by 4 DX ok so here we have to use the formula for integration of Y to the power and TY that is Y to the power n + 1 / n + 1 |

03:00 - 03:59 | using this we have the integration as area is equal to fit 1 1 by 4 outside we have x square by 2 + 2 x minus x cube by 3 and the strangers from -1 to 2 Chunav putting the values we have one by four outside and we have to square by two that is 4 by 2 x 2 + 2 into 2 S4 - 2 cube is 813 minus of minus one square is one by two + 20 - 34 - 2 minus minus 1 cube is minus 1 + 1 by 3 so and calculation this comes out to be 1 by 4 outside |

04:00 - 04:59 | this is 10 by 3 - of this concert B minus 7 by 6 ok or that comes out to be 1 by 4 x on calculation in this we have night bye to so we have the area as 9 by 8 square units ok so this is bar final answer to the question thank you |

**Area as a definite integral**

**Algorithm for area calculation using horizontal strips**

**Area calculation using horizontal strips for modulus function**

**Impact of sign on area definition change according to sign of function**

**Find the area of the region bounded by the parabola `y^2 = 2x` and the line `x - y = 4`**

**Examples: Find the area of the region bounded by the curve `y^2 = 2y - x` and the y-axis.**

**Area of symmetrical graphs**

**Find the area of the region bounded by the ellipse `x^2 / a^2 + y^2 / b^2 = 1`**

**Integration of sin and cos function in different intervals**

**Examples: f(x) = x for x > 0 and f(x) = x^2 for x < 0; find area with x axis from x = -2 and x = 3.**