AMENDMENT NO. 1 TO THE AGREEMENT ANDPLAN OF MERGER

Exhibit 2.2

AMENDMENT NO. 1 TO THE

AGREEMENT AND PLAN OF MERGER

This AMENDMENT NO. 1 TO THE AGREEMENT AND PLAN OF MERGER, dated as of May 18, 2004 (this “Amendment”), is made by and among Whiting Petroleum Corporation, a Delaware corporation (“Parent”), WPC Equity Acquisition Corp., a Colorado corporation and a wholly-owned subsidiary of Parent (“Merger Sub”), and Equity Oil Company, a Colorado corporation (the “Company”). Capitalized terms used in this Amendment and not otherwise defined herein shall have the respective meanings set forth in the Original Agreement (as defined hereinafter).

WHEREAS, Parent, Merger Sub and the Company entered into an Agreement and Plan of Merger, dated as of February 1, 2004 (the “Original Agreement” and as modified hereby, this “Agreement”); and

WHEREAS, Parent, Merger Sub and the Company desire to make certain amendments to the Original Agreement.

NOW, THEREFORE, in consideration of the foregoing and the respective representations, warranties, covenants and agreements, and other good and valuable consideration, set forth herein, the receipt and sufficiency of which are hereby acknowledged, the Parties hereto agree as follows:

ARTICLE I

AMENDMENTS

Section 1.1 The Original Agreement is hereby amended by deleting the second sentence of Section 1.5(d) and inserting, in lieu thereof, the following sentence:

“The Option Termination Agreement shall provide, among other things, that each applicable Company Stock Option shall be cashed out at the difference between the applicable strike price for the Company Stock Option and the average closing price for Parent common stock on the New York Stock Exchange for the five Business Days ending on the Business Day immediately prior to the Closing Date of the Merger multiplied by the Exchange Ratio.”

Section 1.2 The Original Agreement is hereby amended to add the following Section 5.10 which shall read in its entirety as follows:

“SECTION 5.10 REASONABLE BEST EFFORTS TO QUALIFY AS REORGANIZATION

From and after the date of this Agreement and until the Effective Time, each Party hereto shall use its Reasonable Best Efforts to cause the Contemplated Transactions to qualify as a reorganization under the provisions of Section 368(a) of the Code and to satisfy the

conditions or other requirements applicable in connection with the opinion of counsel described in Section 8.7, and will not knowingly take any action, cause any action to be taken, fail to take any action or cause any action to fail or to be taken which action or failure to act could prevent the Contemplated Transactions from qualifying as a reorganization under the provisions of Section 368(a) of the Code, or from satisfying the conditions or other requirements applicable in connection with the opinion of counsel described in Section 8.7. Following the Effective Time, neither the Surviving Corporation, Parent nor any of their Affiliates shall knowingly take any action, cause any action to be taken, fail to take any action or cause any action to fail to be taken, which action or failure to act could cause the Contemplated Transactions to fail to qualify as a reorganization under Section 368(a) of the Code, or would be inconsistent with or be contrary to the conditions or other requirements applicable in connection with the opinion of counsel described in Section 8.7 (including without limitation the representations given by the Surviving Corporation and Parent in connection with such opinion).”

Section 1.3 The Original Agreement is hereby amended to add the following Subsection 9.3(d) which shall read in its entirety as follows:

“(d) Notwithstanding anything herein to the contrary, the Parties agree that the fees and expenses incurred in connection with this Agreement and the Contemplated Transactions (the “Transaction Expenses”) identified on Appendix 1 attached hereto shall be funded by the Party identified as the Party to fund such Transaction Expenses. The Parties acknowledge and agree that the Transaction Expenses set forth on Appendix 1 represent the known categories and the good faith estimates of the Parties of such amounts to be due and payable on or about the Closing Date and that the Parties will modify Appendix 1 as applicable and will fund the actual Transaction Expenses as the same become due, subject to Section 5.10. In connection with the preceding covenants, the Parties additionally agree as follows:

(i) Parent agrees to contribute sufficient funds to Merger Sub as equity capital in an amount sufficient to pay the Transaction Expenses on Appendix 1 to be funded by Parent;

(ii) Merger Sub agrees that it shall maintain such contributed funds in a separate bank account and not commingle such contributed funds with the other funds of Merger Sub or the funds of the Company or the Surviving Corporation;

(iii) Following the Closing, such contributed funds will be used to pay the Transaction Expenses identified on Appendix 1 to be funded by Parent to the extent such Transaction Expenses actually become due and payable;

(iv) For at least 12 months following the Effective Time, the aggregate cash distributions or other cash payments made by the Surviving Corporation to Parent (or any Affiliate of Parent) shall not exceed 50% of the aggregate net income of the Surviving Corporation attributable to periods following the Effective Time; and

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(v) Parent will pay directly, from its funds and not from funds held by the Company prior to the Closing, all costs that Parent has incurred or for which Parent is responsible in connection with the Merger.”

ARTICLE 2

GENERAL PROVISIONS

Section 2.1 Counterparts. This Amendment may be executed in any number of counterparts and by different Parties on separate counterparts, each of which, when executed and delivered, shall be deemed to be an original, and all of which, when taken together, shall constitute but one and the same Amendment. Delivery of an executed counterpart of this Amendment by telefacsimile shall be equally as effective as delivery of an original executed counterpart of this Amendment. Any Party delivering an executed counterpart of this Amendment by telefacsimile also shall deliver an original executed counterpart of this Amendment but the failure to deliver an original executed counterpart shall not affect the validity, enforceability, and binding effect of this Amendment.

Section 2.2 Governing Law. This Amendment shall be construed in accordance with, and governed in all respects by, the laws of the State of Colorado (without giving effect to principles of conflict of law).

Section 2.3 Continuation of Original Agreement. Other than as set forth in this Amendment, all other provisions of the Original Agreement shall remain in full force and effect.

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The Parties have executed and delivered this Amendment as of the date indicated in the first sentence of this Amendment.

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